HW #1

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

For problems #11-#13, (i) classify the variable(s) as qualitative or quantitative, (ii) if it’s quantitative, state whether it’s discrete or continuous.

#11 (text p. 60) Number of new automobiles sold at a dealership on a given day.

 #12 Weight in carats of an uncut diamond.                  #13 Brand name of a pair of running shoes.

 

For problems #16-#19, determine the level (i.e., nominal, ordinal, interval and ratio) of each variable.

#16 Birth year.             #17 Marital status.      #18 Stock rating (strong buy, buy, hold, sell, strong sell).

#19 Number of siblings.

 

For problems #6-#7, (i) determine whether the study is an observational study or a designed experiment. (ii) Identify the response variable in each case.

#6 (text p. 61) A random sample of 30 digital cameras is selected and divided into two groups. One group uses a brand-name battery, while the other uses a generic plain-label battery. All variables besides battery type are controlled. Pictures are taken under identical conditions and the battery life of the two groups is compared.

 #7 A sports reporter asks 100 baseball fans if Barry Bonds’ 756th homerun ball should be marked with an asterisk when sent to the Baseball Hall of Fame.

#4 (text p. 123) Data: Number of cars that arrived at McDonald’s between 11:50AM and noon each Wednesday for the past 50 weeks.

     1   7   3   8   2   3   8   2   6   3   6   5   6   4   3   4   3   8   1   2   5   3   6   3   3   4   3   2   1   2   4   4   9   3   5   2   3   5   5   5   2   5   6   1   7   1   5   3   8   4

     (a) Frequency distribution. (b) Relative frequency distribution. (c) Cumulative frequency distribution. (d) Cumulative relative frequency distribution. (e) Frequency histogram. (f) Relative frequency histogram. *You don’t have to do (g)~(i).

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question. Grab a pencil and indicate (draw a box on the printout, for example) clearly which is (a), (b), etc.

·         No comments = no points!

 

#2.18 (text p. 95) Data: (n=50) number of free throws until a miss.

Number of Free Throws until a Miss

Frequency

1

16

2

11

3

9

4

7

5

2

6

3

7

0

8

1

9

0

10

1

 

(a) Draw a histogram with Minitab.

MTB > hist c1

(b) Draw a histogram with 5 classes.

MTB > hist c1;                               (Don’t forget semicolon.)

SUBC> nint 5.                                 (Don’t forget the period at the end.)

                (c) Is it a symmetrical distribution or skewed? If skewed, which way?

(d) The two histograms of (a) and (b) give a somewhat a different impression. Which one give you less skewed distribution?

(e) What percentage of the time did she first miss on her fourth free throw?

(f) What percentage of the time did she make at least five in a row?

HW #2

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          The weight gains of beef steers were measured over a 140-day test period. The average daily gains (lb/day) of 9 steers on the same diet were as follows:

3.89        3.51        3.97        3.31        3.21        3.36        3.67        3.24        3.27

Find the mean and median.

 

#2.          In a study of milk production in sheep (for use in making cheese), a researcher measured the three-month milk yield for each of 11 ewes. The yields (liters) were as follows:

56.5        89.8        110.1      65.6        63.7        82.6        75.1        91.5        102.9      44.4        108.1

(a)   Determine the median and the quartiles.

(b)   Determine the interquartile range.

(c)   Construct a boxplot of the data. Be sure to clearly indicate any outlier(s).

 

#3.          Calculate the standard deviation of each of the following fictitious samples:

                (a)   16, 13, 18, 13                               (b) 38, 30, 34, 38, 35

                (c)   1, -1, 5, -1                                      (d) 4, 6, -1, 4, 2

 

#4.          A biologist made a certain pH measurement in each of 24 frogs; typical values were

7.43,  7.16,  7.51,...

She calculated a mean of 7.373 and a standard deviation of .129 for these original pH measurements. Next, she transformed the data by subtracting 7 from each observation and then multiplying by 100. For example, 7.43 was transformed to 43.The transformed data are

43,  16,  51,...

What are the mean and standard deviation of the transformed data?

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#5. Data: (n=31) Number of malarial parasites per 1 ml of blood.

  100       140       140       271       400       435       455       770

  826      1400      1540      1640      1920      2280      2340      3672

 4914      6160      6560      6741      7609      8547      9560     10516

14960     16855     18600     22995     29800     83200    134232

 

(a) Draw a histogram with incrementing by 10,000. You don’t need to do a frequency table.

MTB > hist c1;                                               (Don’t forget semicolon.)

SUBC> midp 0:150000/10000.   (Don’t forget the period at the end.)

(b) Draw a histogram after transforming the data by log10. You don’t need to do a frequency table. Now comment on how the transformation affects the shape of the distribution. No comments = no points.

MTB > logten c1 c2         (or     MTB > let c2 = logten(c1))

MTB > hist c2

 

(c) Is the mean of log-transformed data the same as the log of the mean?

(d) Is the median of log-transformed data the same as the log of the median?

 

MTB > let k1=logten(mean(c1))

MTB > prin k1              (This is the log10 of the mean.)

MTB > let k2=logten(median(c1))

MTB > prin k2              (This is the log10 of the median.)

 

 

HW #3

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          In a certain college, 55% of the students are women. Suppose we take a sample of 2 students. Use a probability tree to find the probability

(a)   that both chosen students are women.

(b)   that at least one of the two students is a woman.

 

#2.          In the following data "stressed" means that the person reported that most days are extremely stressful or quite stressful; "not stressed" means that the person reported that most days are a bit stressful, not very stressful, or not at all stressful.

                                                                                    Income

 

Low

Medium

High

Total

Stressed

526

274

216

1016

Not Stressed

1954

1680

1899

5533

Total

2480

1954

2115

6549

(a)   What is the probability that someone in this study is stressed?

(b)   What is the probability that someone in this study has low income?

(c)   What is the probability that someone in this study either is stressed or has low income (or both)?

(d)   What is the probability that someone in this study is stressed and has low income?

 

#15. (text p. 325) The US Senate Appropriations Committee has 29 members and a subcommittee is to be formed by randomly selecting 5 of its members. How many different committees could be formed? Show work.

 

#16. In Pennsylvania’s Cash 5 lottery, balls are numbered 1 to 43. Five balls are randomly selected without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability of winning Pennsylvania’s Cash 5 with one ticket. Show all your work. Answer alone = no points!

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

Ex #1, #2, #3 (notes p. 93) Execute the following string of commands 100 times and answer #1, #2, & #3.

Empirical P(at least two with the same birthday) = (# of groups with at least two having same birthday) ¸ 100

Theoretical P(at least two with the same birthday)=see notes p.93.

Turn in the output of all 100 groups of 23 people’s birthday with each case classified into “Yes” or “No” cases. Edit the printout so we can save paper.

In a group of 23 people,

Probability(at least 2 with the same birthday)

= 1 - Prob (no one with the same birthday)

=

= 0.5

 

 

 

 

HW #4

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          A group of college students were surveyed to learn how many times they had visited a dentist in the previous year. The probability distribution for Y, the number of visits, is given by the following table;

Y (Number of visits)

Probability

0

0.15

1

0.50

2

0.35

Calculate the mean, mY, of the number of visits, and the standard deviation, sY, of the random variable Y.

 

#2.          The seeds of the garden pea (Pisum sativum) are either yellow or green. A certain cross between pea plants produces progeny in the ratio 3 yellow :1 green. If four randomly chosen progeny of such a cross are examined, what is the probability that

(a) three are yellow and one is green?

(b) all four are yellow?

(c) all four are the same color?

 

#3. (text p. 368)

X (Number of sets played at Wimbledon Tennis Championship)

Frequency

3

18

4

10

5

12

(a)     Probability model, (b) Probability histogram, (c) Compute the mean, (d) Compute the SD.

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

Ex #1, #2, #3 (notes p. 97) Indicate which part of the printout answers #1, #2, &#3.

MTB > set c1

DATA> -1 4 9 99

DATA> end

MTB > set c2

DATA> 0.885 0.1 0.014 0.001

DATA> end

MTB > let c3=(c1*c2)              This is the formula to calculate the mean m.

MTB > sum c3

   Sum of C3 = -0.26000           m

MTB > let c4=((c1+0.26)**2)*c2    This is the formula to calculate the SD s.

MTB > let k1=sqrt(sum(c4))

MTB > prin k1

K1    3.65409                     s

MTB > rand 200 c5;                Simulating 200 from the underlying probability distribution.

SUBC> disc c1 c2.

MTB > desc c5                     Find  and s.

MTB > hist c5                     This draws a histogram of the 200 samples.

 

Sample mean and sample SD are supposed to be close to the (theoretical) population mean and SD, respectively. Is that really the case here? If not, comment on why?

 

 

HW #5

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#8. (text p. 368) (Show all your work. Answer alone = no points!) 35% of the participants who took the drug Zyban experienced insomnia. In a random sample of 25 users of Zyban, find the probability that

(a) exactly 8 will experience insomnia

(b) fewer than 4 will experience insomnia

(c) at least 5 will experience insomnia

(d) exactly 20 will not experience insomnia.

(e) In a random sample of 1,000 users of Zyban, what is the expected number who experience insomnia? What is the SD?

(f) If a random sample of 1,000 users of Zyban results in 330 who experience insomnia, would this be unusual? Why?

 

#1.          The shell of the land snail Limocolaria martensiana has two possible color forms. streaked and pallid. In a certain population of these snails, 60% of the individuals have streaked shells. Suppose that a random sample of 10 snails is to be chosen from this population.

(a) What is the mean number of streaked-shelled snails?

(b) What is the standard deviation of the number of streaked-shelled snails?

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

Ex #1, #2, #3, #4 (notes p. 101)

MTB > set c1

DATA> 0:12

DATA> end

MTB > pdf c1 c2;

SUBC> bino 12 0.8.

MTB > cdf c1 c3;

SUBC> bino 12 0.8.

MTB > print c1 c2 c3                       This creates the pdf and cdf table.

MTB > plot c2*c1 c3*c1;

SUBC> over.                                                      This creates the pdf and cdf graph overlaid.

MTB > cdf 9;

SUBC> bino 12 0.8.                This gives the cdf of 9 for a binomial(12, 0.8).

MTB > rand 80 c5;

SUBC> bernoulli 0.542.

MTB > tally c5                           Simulation of 80 games: 1=win, 0=loss.

MTB > random 1000 c7;

SUBC> bino 6 0.5.

MTB > hist c7

MTB > tally c7                                    This is the result of your simulation of 1,000 families’ survey.

MTB > pdf 6;

SUBC> bino 6 0.5.                          This gives the (theoretical) probability of 6 (i.e., families with all girls).

MTB > cdf 2;

SUBC> bino 6 0.5.                                        This gives the (theoretical) cdf of 2 (i.e., families with more boys).

Simulated numbers are supposed to be quite close to the (theoretically) expected numbers. Is that really the case here?

 

 

 

HW #6

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          The heights of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm. What percentage of the plant heights are

(a) 100 cm or more?                           (b) 120 cm or less?              (c) between 120 and 150 cm?

(d) between 100 and 120 cm?          (e) between 150 and 180 cm?

(f) 180 cm or more?                            (g) 150 cm or less?

 

#2.          Suppose four plants are to be chosen at random from the corn plant population of Exercise #1. Find the probability that none of the four plants will be more than 150 cm tall.

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

Ex #1, #2, #3, #4 (notes p. 109)

MTB > set c1

DATA> -3.5:3.5/0.02

DATA> end

MTB > pdf c1 c2

MTB > plot c2*c1;

SUBC> conn.                       This draws the standard normal pdf.

MTB > set c3

DATA> 0:48/0.05

DATA> end

MTB > pdf c3 c4;

SUBC> norm 24 8.

MTB > plot c4*c3;

SUBC> conn.                       This draws the normal pdf with mean24, and SD 8.

MTB > rand 500 c6;

SUBC> norm 24 8.

MTB > sort c6 c7                  Both C6 and C7 hold random numbers from normal 24, 8.

MTB > desc c6

MTB > pplot c6                    Use “drop down” menu to draw NPP of C6

MTB > cdf 120;

SUBC> norm 115 5.

MTB > cdf 95;

SUBC> norm 115 5.                 You have to subtract the latter from the former to get the “between” prob.

MTB > set c9

DATA> 28 27 29 29 30 30 31 30 33 27 30 32

DATA> end

MTB > pplot c9                    Use “drop down” menu to draw NPP of C9

For problem #2, you need to print C7 and comment if the 68-95-99.7 rule applies here.

 

 

 

 

 

 

 

 

 

 

 

HW #7

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          The heights of a certain population of corn plants follow a normal distribution with mean 145 cm and standard deviation 22 cm.

(a) What percentage of the plants are between 135 and 155 cm tall?

(b) Suppose we were to choose at random from the population a large number of samples of 16 plants each. In what percentage of the samples would the sample mean height be between 135 and 155 cm?

(c) If  represents the mean height of a random sample of 16 plants from the population, what is Pr{135155}?

(d) If  represents the mean height of a random sample of 36 plants from the population, what is Pr{135155}?

 

#2.          As part of a study of the development of the thymus gland, researchers weighed the glands of five chick embryos after 14 days of incubation. The thymus weights (mg) were as follows:

29.6       21.5       28.0       34.6       44.9

                For these data, the mean is 31.7 and the standard deviation is 8.7.

(a) Calculate the standard error of the mean.

(b) Construct a 90% confidence interval for the population mean.

 

#3.          To study the conversion of nitrite to nitrate in the blood, researchers injected four rabbits with a solution of radioactively labeled nitrite molecules. Ten minutes after injection, they measured for each rabbit the percentage of the nitrite that had been converted to nitrate. The results were as follows:

51.1       55.4       48.0       49.5

(a)           For these data, calculate the mean, the standard deviation, and the standard error of the mean.

(b)           Construct a 95% confidence interval for the population mean percentage.

(c)           Without doing any calculations, would a 99% confidence interval be wider, narrower, or the same width as the confidence interval you found in part (b)? Why?

Computer Exercise

Ex #1, #2, #3, #4 , #5 (notes p. 115)

MTB > invcdf 0.95;

SUBC> t 10.                       This is how you can find t0.05(df=10), for example.

MTB > invcdf 0.95;

SUBC> norm 0 1.                   This is how you can find Z0.05.

MTB > invcdf 0.95;

SUBC> chisq 10.                   This is how you can find (df=10), for example.

MTB > rand 1000 c1;

SUBC> t 20.                       Simulating 1,000 numbers from tdf=20, for example.

MTB > desc c1

MTB > hist c1

MTB > rand 1000 c2;

SUBC> chisq 20.                                             Simulating 1,000 numbers from .

MTB > desc c2

MTB > hist c2

Hints:     #4 (c) (Theoretical) population mean m = 0, Theoretical SD s = .

                #5 (c) (Theoretical) population mean m = df = 20, Theoretical SD s = .

HW #8

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          The accompanying table summarizes the sucrose consumption (mg in 30 minutes) of black blowflies injected with Pargyline or saline (control).

 

 

Control

Pargyline

n

900

905

14.9

46.5

s

5.4

11.7

 

Compute (a) a 95% confidence interval, (b) a 99% confidence interval for the difference in population means. Note: Welch-Satterthwaite’s df yields 1,274 degrees of freedom for these data.

 

#2.          A researcher investigated the effect of green light, in comparison to red light, on the growth rate of bean plants. The following table shows data on the heights of plants (in inches), from the soil to the first branching stem, two weeks after germination.

 

Red

8.4    8.4   10.0    8.8    7.1    9.4    8.8    4.3    9.0    8.4    7.1    9.6    9.3    8.6    6.1    8.4   10.4

Green

8.6    5.9    4.6    9.1    9.8   10.1    6.0   10.4   10.8    9.6   10.5   9.0    8.6   10.5    9.9   11.1    5.5    8.2    8.3   10.0    8.7    9.8    9.5   11.0    8.0

 

 

Red

Green

N

17

25

8.36

8.94

s

1.5

1.78

SE

0.36

0.36

 

Use these data to construct a 95% confidence interval for the difference in mean effect that red light has on bean plant growth, in comparison to green light Note: Welch-Satterthwaite’s df yields 38 degrees of freedom for these data.

 

#3.          The following figures are the milk fat concentration (g/kg).

30.5         28.7         27.3         24.1         42.3         35.7         32.7         41.5         20.5         36.3

25.5         30.9         34.6         35.1         26.3         33.6         31.9         34.7         35.0         35.9

33.3         34.5         30.6         34.0         38.2         42.5         37.4         33.3         40.3         21.7

                Find a 95% c.i. for the m, the true milk fat concentration.

 

Computer Exercise

 

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#4.          The following figures refer to the cardiac outputs of 29 patients.

2.60   5.16   6.18   3.22   4.99   3.62   5.40   5.93   3.31   4.11

5.24   4.27   3.42   4.70   5.90   4.11   5.42   5.36   2.63   3.70

5.39   5.44   4.44   2.64   3.86   6.68   5.35   3.26   4.06

(a)     Construct a 95% c.i. for the true mean cardiac output for patients of this type.

(b)     At 0.05, is the true mean cardiac output significantly greater than 4.0? Justify your answer.

(c)     Is the normal distribution assumption safe? Comment on why do we want to check on this?

MTB > tint 95 c1

MTB > ttest 4.0 c1;

SUBC> alte 1.              This is how you ask for the 1-tail test.

 

 

 

 

HW #9

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          For each of the following situations, suppose H0:  is being tested against HA: . State whether or not H0 would be rejected.

(a) P-value = .085,               a = 0.10

(b) P-value = .065,               a  = 0.05

(c) ts = 3.75 with 19 degrees of freedom, a  = 0.01

(d) ts = 1.85 with 12 degrees of freedom, a  = 0.05

 

#2.          In a study of the nutritional requirements of cattle, researchers measured the weight gains of cows during a 78-day period. For two breeds of cows, Hereford (HH) and Brown Swiss/Hereford (SH), the results are summarized in the following table. Note. Welch-Satterthwaite’s df yields 71.9 df.

 

 

HH

SH

n

33

51

18.3

13.9

s

17.8

19.1

 

Use a t test to compare the means. Use a = 0.05.

 

#3.          Suppose we have conducted a t test, with a = 0.05, and the P-value is 0.03. For each of the following statements, say whether the statement is true or false and explain why.

(a) We reject H0 with a = 0.05.

(b) We would reject H0 if a were 0.10.

(c) If H0 is true, the probability of getting a test statistic at least as extreme as the value of the ts that was actually obtained is 3%.

 

#4.          Suppose in a test, the null hypothesis was not rejected. Then what type of error, Type I or Type II, might have been made in that test?

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#5. Data: (n1=14, n2=10) GITH activities. Run a 2-tail t-test at a=0.05. Don’t forget to state conclusion in plain terms.

 

Low-Chromium Diet:   42.3     51.5     53.7     48.0     56.0     55.7     54.8

                     52.8     51.3     58.5     55.4     38.3     54.1     52.1

Normal Diet:         53.1     50.7     55.8     55.1     47.5     53.6     47.8

                     61.8     52.6     53.7

<<< Note: Data are in 1,000 counts per minute per gram of liver sample (cpm). >>>

MTB > twos c1 c2;

SUBC> pool.

 

#6. Data: (n1=15, n2=15) Distances (in meters) lizards ran in two minutes.

(a) 1-tail t-test at a=0.05. (b) 2-tail t-test at a=0.05.

Infected lizards:    16.4     29.4     37.1     23.0     24.1     24.5     16.4

                     29.1     36.7     28.7     30.2     21.8     37.1     20.3

                     28.3

Uninfected lizards:  22.2     34.8     42.1     32.9     26.4     30.6     32.9

                     37.5     18.4     27.5     45.5     34.0     45.5     24.5

                     28.7

 

 

 

HW #10

 

*              Be sure to write your name.

*              For any statistical hypothesis tests, don’t forget to write (your hand writing!) H0, H1, test-statistic, p-value, and conclusion in plain terms. Each of these items will be graded separately!

*              Show all your work! No work = no points.

 

#1.          In an experiment to compare two diets for fattening beef steers, nine pairs of animals were chosen from the herd; members of each pair were matched as closely as possible with respect to hereditary factors. The members of each pair were randomly allocated, one to each diet. The following table shows the weight gains (lb) of the animals over a 140-day test period on diet 1 (Y1) and on diet 2 (Y2).

 

Pair

Diet 1

Diet 2

Difference

1

596

498

98

2

422

460

-38

3

524

468

56

4

454

458

-4

5

538

530

8

6

552

482

70

7

478

528

-50

8

564

598

-34

9

556

456

100

Mean

520.4

497.6

22.9

SD

57.1

47.3

59.3

 

(a)   Calculate the standard error of the mean difference.

(b)   Test for a difference between the diets using a paired t test at a = 0.05. Use a 1-tailed test.

(c)   Construct a 95% confidence interval for md.

(d)   Interpret the confidence interval from part (c) in the context of this setting.

 

#2.          As part of the study involving the compound mCPP, weight change was measured for nine men. For each man two measurements were made: weight change when taking mCPP and weight change when taking the placebo. The data are given in the accompanying table. Analyze these data with an appropriate t-test at the a = 0.05 level; use a 1-tailed alternative. Don’t forget to write H0, H1, test-statistic, p-value, and conclusion in plain terms.

 

                                Weight Change

Subject

mCPP (Y1)

Placebo (Y2)

Difference (d = Y1 - Y2)

1

0.0

-1.1

1.1

2

-1.1

0.5

-1.6

3

-1.6

0.5

-2.1

4

-0.3

0.0

-0.3

5

-1.1

-0.5

-0.6

6

-0.9

1.3

-2.2

7

-0.5

-1.4

0.9

8

0.7

0.0

0.7

9

-1.2

-0.8

-0.4

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#3. (notes p. 124) Data: (n1=20, n2=20) Run a paired t-test (two-tailed) at a=0.05.

MTB > ttest c3

                Don’t forget to write (your hand writing!) H0, H1, test-statistic, p-value, and conclusion in plain terms.

 

 

HW #11

 

*              Be sure to write your name.

*              For any statistical hypothesis tests, don’t forget to write (your hand writing!) H0, H1, test-statistic, p-value, and conclusion in plain terms. Each of these items will be graded separately!

*              Show all your work! No work = no points.

 

#1.          A cross between white and yellow summer squash gave progeny of the following colors:

 

Color

White

Yellow

Green

Number of progeny

155

40

10

 

Are these data consistent with the 12:3:1 ratio predicted by a certain genetic model? Use a chi square test at a = 0.05.

 

#2.          In a breeding experiment, white chickens with small combs were mated and produced 190 offspring, of the types shown in the accompanying table. Are these data consistent with the Mendelian expected ratios of 9:3:3:1 for the four types? Use a chi-square test at a = 0.05.

 

Type

Number of Offspring

White feathers, small comb

111

White feathers, large comb

37

Dark feathers, small comb

34

Dark feathers, large comb

8

Total

190

 

 

#3.          An ecologist studied the spatial distribution of tree species in a wooded area. From a total area of 21 acres, he randomly selected 144 quadrats (plots), each 38 feet square, and noted the presence or absence of maples and hickories in each quadrat. The results are shown in the table.

                                                                                Maples

 

 

Present

Absent

 

 

 

Hickories

 

Present

26

63

 

 

 

 

 

Absent

29

26

 

 

 

 

 

 

 

 

 

 

Test the null hypothesis that the two species are distributed independently of each other.

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#4. Data: (n=78) Color and the time of the year clams died. Perform a c2 test if the distribution of colors differs between the two months.

                                                                                                                  Color

 

 

Clear

Dark

Unreadable

Months

February

9

26

9

 

March

6

25

3

 

#5. Data: (n=83) Drug treatment and condition of patients. Perform a c2 test if the treatment group and condition are significantly related.

                                                                                                                Condition

 

 

No Response

Moderate Resp

Marked Resp

Remission

Treatmnt

Fluvoxamine

15

7

3

15

 

Placebo

22

7

3

11

 

 

 

HW #12

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          The accompanying table shows fictitious data for three samples.

                                                                                                Sample

 

I

II

III

 

48

40

39

 

39

48

30

 

42

44

32

 

43

 

35

Mean

43

44

34

 

(a) Write the null and alternative hypotheses.

(b) State the requirements that must be satisfied to use the 1-way ANOVA procedure.

(c) Construct a 1-way ANOVA table and test the hypothesis of equal means at a = 0.05 level of significance.

 

#2.          The following ANOVA table is only partially completed.

 

Source

SS

DF

MS

F

p-value

Factor

____________

3

45

_________

_________

Error

337

12

___________

 

 

Total

472

___

 

 

 

 

(a) Complete the table.

(b) How many treatment groups were there in the study?

(c) How many total observations were there in the study?

 

#3.          The computer output below is for an analysis of variance in which yields (bu/acre) of different varieties of oats were compared.

 

Source

SS

DF

MS

F

p-value

Factor

76.895

2

38.4475

0.40245

0.6801

Error

859.808

9

95.5342

 

 

Total

936.703

11

 

 

 

 

(a) Write the null and alternative hypotheses.

(b) How many varieties (groups) were in the experiment?

(c) State the conclusion of the ANOVA.

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#13. (text p. 690) Are there more live births during the week than on weekends?

 

Monday

Tuesday

Wednesday

Thursday

Friday

10456

11621

12084

11171

11545

10023

11944

11570

11745

12321

10691

11045

11346

12023

11749

10283

11927

11875

12433

12192

10265

12577

12193

12132

12422

11189

11753

11593

11903

11627

11198

12509

11216

11233

11624

11465

12521

11818

12543

12543

 

(a) Write the null and alternative hypotheses.

(b) State the requirements that must be satisfied to use the 1-way ANOVA procedure.

(c) Run a 1-way ANOVA procedure and state the conclusion in plain terms.

 

 

HW #13

 

*              Be sure to write your name.

*              Show all your work! No work = no points.

 

#1.          A botanist used a completely randomized design to allocate 45 individually potted eggplant plants to five different soil treatments. The observed variable was the total plant dry weight without roots (g) after 31 days of growth. The treatment means were as shown in the table. The MSE was 0.2246. Use Tukey’s test to compare all pairs of means at a = 0.05 and write the conclusion using the line notation.

 

Treatment

A

B

C

D

E

Mean

4.37

4.76

3.70

5.41

5.38

n

9

9

9

9

9

 

#2.          In a study of the dietary treatment of anemia in cattle, researchers randomly divided 144 cows into four treatment groups. Group A was a control group, and groups B, C, and D received different regimens of dietary supplementation with selenium. After a year of treatment, blood samples were drawn and assayed for selenium. The accompanying table shows the mean selenium concentrations (mg/d/Li). The MSE from the ANOVA was 2.071, Use Tukey’s test to compare all pairs of means at a = 0.05 and write the conclusion using the line notation.

 

Group

A

B

C

D

Mean

0.8

5.4

6.2

5.0

n

36

36

36

36

 

Computer Exercise

·         Print your name on the first page of the computer printout.

·         Do not just turn in computer printouts. You must indicate which printout answers what question.

 

#3.          There is a hypothesis that the birthweight of an infant is associated with the smoking status of the mother during the first trimester of pregnancy. To test this hypothesis, data were collected on pregnant women in a prenatal clinic and birthweights were recorded for their newborns. The mothers were also classified into four groups as follows:

Group 1.

Mother has never smoked.

Group 2.

Mother is an ex-smoker, but did not smoke during pregnancy.

Group 3.

Mother is a current smoker and smokes less than 1 pack/day.

Group 4.

Mother is a current smoker and smokes at least 1 pack/day.

The data were as follows.

Group 1.

7.5     6.2     6.9     7.4     9.2     8.3     7.6

Group 2.

5.8     7.3     8.2     7.1     7.8

Group 3.

5.9     6.2     5.8     4.7     8.3     7.2     6.2

Group 4.

6.2     6.8     5.7     4.9     6.2     7.1     5.8     5.4

(a)   Draw a side-by-side boxplot (i.e., schematic plot). Note that the variances are not much different.

(b)   Run a 1-way ANOVA to see if there is a significant difference in mean birth weights in the four groups. And state your conclusion.

(c)   Use Tukey’s test and determine which pairwise means differ and write your conclusion in line notation. State your conclusion in plain terms.

 

 

 

 

HW #14

 

#2. (text p. 784) Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following table lists the temperature (in Fahrenheit, °F) and the number of chirps per second for the striped ground cricket.

 

Temperature (x)

Chirps per second (y)

88.6

20

93.3

19.8

80.6

17.1

69.7

14.7

69.4

15.4

79.6

15

80.6

16

76.3

14.4

71.6

16

84.3

18.4

75.2

15.5

82.0

17.1

83.3

16.2

82.6

17.2

83.5

17

(a)   Find the estimates of  and . What is the mean number of chirps when the temperature is 80.2°F?

(b)   Find the SE of the estimate, .

(c)   Are the residuals normally distributed?

(d)   If the residuals are normally distributed, determine .

(e)   If the residuals are normally distributed, test whether the linear relationship exists between the explanatory variable, x, and the response variable, y, at the  level of significance.

(f)    If the residuals are normally distributed, construct a 95% c.i. for the slope of the true least-squares regression line.

(g)   Construct a 90% c.i. for the mean number of chirps found in part (a).

(h)   Predict the number of chirps on a day when the temperature is 80.2°F?

(i)    Construct a 90% p.i. for the number of chirps found in part (h).

(j)    Explain why the predicted number of chirps found in parts (g) and (i) are the same, yet the intervals are different.

Computer Exercise

#4. (text p. 784) A researcher believes that as age increases the grip strength (pounds per square inch, psi) of an individual’s dominant hand decreases. From a random sample of 17 females, he obtains the following data:

 

Age (x)

Grip Strength (y)

15

65

16

60

28

58

61

60

53

46

43

66

16

56

25

75

28

46

34

45

37

58

41

70

43

73

49

45

53

60

61

56

68

30

 

(a)   Find the estimates of  and .

(b)   Find the SE of the estimate, .

(c)   Are the residuals normally distributed?

(d)   If the residuals are normally distributed, determine .

(e)   If the residuals are normally distributed, test whether the linear relationship exists between the explanatory variable, x, and the response variable, y, at the  level of significance.

(f)    Based on your answers to (d) and (e), what would be a good estimate of the grip strength of a randomly selected 42-year-old female?