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1. Vegetarians and Omnivores. Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarXXXXX XXXXXfestyle. A study by Lu et al., published in the Journal of Nutrition (Vol. 130, pp. 1591-1596), compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan. Among the nutrients considered was protein. Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. Independent random samples of 51 female vegetarians and 53 female omnivores yielded the data, in grams, on daily protein intake presented in the Chapter 10 data sets, problem #10.51. Do the data provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level.

a. Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA). Two sample T Statistics

b. State the null and alternative hypotheses.

U1 = mean of vegetarians

U2 = mean of omnivores

Ho: u1 = u2

Ha: u1 does not equal u2

c. Use StatCrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.) What is the value of the test statistic that you obtained from the software?

Sample mean -10.885313

Standard error 3.7065785

Df 102

T-Stat -2.936755

d. What is the p-value obtained from the software? 0.0041

e. What is your conclusion?

2. Anorexia Treatment. Anorexia nervosa is a serious eating disorder, particularly among young women. The data in Chapter 10 data sets, problem #10.143, provides the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa. [SOURCE: Hand et al. (ed.) A Handbook of Small Data Sets, London: Chapman & Hall, 1994.] Does family therapy appear to be effective in helping anorexic young women gain weight? Perform the appropriate hypothesis test at the 5% significance level.

a. Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA)

Inferences for two population means, using paired samples

Paired T-interval procedure

b. State the null and alternative hypotheses.

U1-u2: mean of paired difference between before and after

Ho: u1-u2=0

Ha: u1-u2 does not equal 0

c. Use Statcrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.) What is the value of the test statistic that you obtained from the software?

Sample difference -7.2647057

Standard error 1.7359296

Df 16

T-Stat -4.184908

d. What is the p-value obtained from the software? 0.0007

e. What is your conclusion?

3. Staph Infections. In an article in the Journal of Statistics Education, Vol. 12, No.2, N. Binnie analyzes bacteria-culture data collected by Gavin Cooper at the Auckland University of Technology. Five strains of cultured Staphylococcus aureus – bacteria that cause staph infections – were observed for 24 hours at 27 degrees Celsius. The data in Chapter 16 data sets, problem #16.51, reports bacteria counts, in millions, for different cases from each of the five strains. (Note: You will only need the first five columns of data in this spreadsheet – you do not need the columns called COUNT and STRAIN.) At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean bacteria counts among the five strains of Staphylococcus aureus?

a. Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA).

One-Way ANOVA procedure

b. State the null and alternative hypotheses.

u1= Strain A

u2= Strain B

u3= Strain C

u4= Strain D

u5= Strain E

Ho: u1=u2=u3=u4=u5

Ha: Not all the means are equal

c. Use Statcrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.) What is the value of the test statistic that you obtained from the software?

n Mean Standard deviation Standard error

Strain A 5 20.8 8.467583 3.7868192

Strain B 5 25.8 17.626684 7.882893

Strain C 5 37 18.330303 8.19756

Strain D 5 19.6 5.683309 2.541653

Strain E 5 38.8 12.617448 5.6426945

ANOVA table ----

Df SS MS F-Stat

Treatments 4 1620.4 405.1 2.2260687

Error 20 3639.3 181.98

Total 24 5260

d. What is the p-value obtained from the software? 0.1027

e. What is your conclusion?

1. Vegetarians and Omnivores. Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarXXXXX XXXXXfestyle. A study by Lu et al., published in the Journal of Nutrition (Vol. 130, pp. 1591-1596), compared the daily intake of nutrients by vegetarians and omnivores living in Taiwan. Among the nutrients considered was protein. Too little protein stunts growth and interferes with all bodily functions; too much protein puts a strain on the kidneys, can cause diarrhea and dehydration, and can leach calcium from bones and teeth. Independent random samples of 51 female vegetarians and 53 female omnivores yielded the data, in grams, on daily protein intake presented in the Chapter 10 data sets, problem #10.51. Do the data provide sufficient evidence to conclude that the mean daily protein intakes of female vegetarians and female omnivores differ? Perform the required hypothesis test at the 1% significance level.

a. Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA). Two sample T Statistics

b. State the null and alternative hypotheses.

U1 = mean of vegetarians

U2 = mean of omnivores

Ho: u1 = u2

Ha: u1 does not equal u2

c. Use StatCrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.) What is the value of the test statistic that you obtained from the software?

Sample mean -10.885313

Standard error 3.7065785

Df 102

T-Stat -2.936755

d. What is the p-value obtained from the software? 0.0041

e. What is your conclusion?

2. Anorexia Treatment. Anorexia nervosa is a serious eating disorder, particularly among young women. The data in Chapter 10 data sets, problem #10.143, provides the weights, in pounds, of 17 anorexic young women before and after receiving a family therapy treatment for anorexia nervosa. [SOURCE: Hand et al. (ed.) A Handbook of Small Data Sets, London: Chapman & Hall, 1994.] Does family therapy appear to be effective in helping anorexic young women gain weight? Perform the appropriate hypothesis test at the 5% significance level.

a. Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA)

Inferences for two population means, using paired samples

Paired T-interval procedure

b. State the null and alternative hypotheses.

U1-u2: mean of paired difference between before and after

Ho: u1-u2=0

Ha: u1-u2 does not equal 0

c. Use Statcrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.) What is the value of the test statistic that you obtained from the software?

Sample difference -7.2647057

Standard error 1.7359296

Df 16

T-Stat -4.184908

d. What is the p-value obtained from the software? 0.0007

e. What is your conclusion?

3. Staph Infections. In an article in the Journal of Statistics Education, Vol. 12, No.2, N. Binnie analyzes bacteria-culture data collected by Gavin Cooper at the Auckland University of Technology. Five strains of cultured Staphylococcus aureus – bacteria that cause staph infections – were observed for 24 hours at 27 degrees Celsius. The data in Chapter 16 data sets, problem #16.51, reports bacteria counts, in millions, for different cases from each of the five strains. (Note: You will only need the first five columns of data in this spreadsheet – you do not need the columns called COUNT and STRAIN.) At the 5% significance level, do the data provide sufficient evidence to conclude that a difference exists in mean bacteria counts among the five strains of Staphylococcus aureus?

a. Determine and state the type of test that should be performed to answer the above question (two sample t-test, paired t-test, or ANOVA).

One-Way ANOVA procedure

b. State the null and alternative hypotheses.

u1= Strain A

u2= Strain B

u3= Strain C

u4= Strain D

u5= Strain E

Ho: u1=u2=u3=u4=u5

Ha: Not all the means are equal

c. Use Statcrunch or SPSS software to perform the hypothesis test. (NOTE: If you choose two sample t-test for this problem, assume that the standard deviations of the two groups are equal and it is appropriate to use pooled t procedures.) What is the value of the test statistic that you obtained from the software?

n Mean Standard deviation Standard error

Strain A 5 20.8 8.467583 3.7868192

Strain B 5 25.8 17.626684 7.882893

Strain C 5 37 18.330303 8.19756

Strain D 5 19.6 5.683309 2.541653

Strain E 5 38.8 12.617448 5.6426945

ANOVA table ----

Df SS MS F-Stat

Treatments 4 1620.4 405.1 2.2260687

Error 20 3639.3 181.98

Total 24 5260

d. What is the p-value obtained from the software? 0.1027

e. What is your conclusion?

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