Question

A multimedia program designed to improve dietary behavior among low-income women was evaluated by comparing women who were randomly assigned to intervention and control groups. The intervention was a 30-minute session in a computer kiosk in the Food Stamp office. One of the outcomes was the score on a knowledge test taken about 2 months after the program. Here is a summary of the data:

Group	n	x	s
Intervention	164	5.11	1.15
Control	216	4.27	1.16

(a) The test had six multiple-choice items that were scored as correct or incorrect, so the total score was an integer between 0 and 6. Do you think that these data are Normally distributed? Explain why or why not.

The distribution is Normal because the standard deviation is smaller than the mean.

The distribution is not Normal because the sample included only women.    

The distribution is not Normal because all scores are integers.

The distribution is Normal because the sample sizes are large.

The distribution is Normal because the sample was randomly assigned.

(b) Is it appropriate to use the two-sample t procedures that we studied in this section to analyze these data? Give reasons for your answer.

The t procedures should be appropriate because we have two large samples with no outliers.

The t procedures should not be appropriate because we do not have Normally distributed data.    

The t procedures should not be appropriate because the two groups are different sizes.

The t procedures should not be appropriate because the sample sizes are not large enough.

The t procedures should be appropriate because we have Normally distributed data.

(c) Describe appropriate null and alternative hypotheses for evaluating the intervention.

H₀: μ_Intervention ≠ μ₂; H_a: μ_Intervention > μ_Control (or μ_Intervention = μ_Control)

H₀: μ_Intervention = μ₂; H_a: μ_Intervention < μ_Control (or μ_Intervention ≠ μ_Control)

H₀: μ_Intervention ≠ μ₂; H_a: μ_Intervention < μ_Control (or μ_Intervention = μ_Control)

H₀: μ_Intervention = μ₂; H_a: μ_Intervention > μ_Control (or μ_Intervention ≠ μ_Control)

H₀: μ_Intervention = μ₂; H_a: μ_Intervention > μ_Control (or μ_Intervention < μ_Control)

Some people would prefer a two-sided alternative in this situation while others would use a one-sided significance test. Give reasons for each point of view.

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would increase scores on the test.

The two-sided alternative allows for the possibility that the intervention might have had a negative effect.

The two-sided alternative reflects the researchers' (presumed) belief that the intervention would decrease scores on the test. The one-sided alternative allows for the possibility that the intervention might have had a positive effect.    

The two-sided alternative reflects the researchers' (presumed) belief that the intervention would increase scores on the test. The one-sided alternative allows for the possibility that the intervention might have had a negative effect.

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would decrease scores on the test. The two-sided alternative allows for the possibility that the intervention might have had a negative effect.

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would decrease scores on the test. The two-sided alternative allows for the possibility that the intervention might have had a positive effect.

(d) Carry out the significance test using a one-sided alternative. Report the test statistic with the degrees of freedom and the P-value. (Round your test statistic to three decimal places, your degrees of freedom to the nearest whole number, and your P-value to four decimal places.)

t	=
df	=
P-value	=

Write a short summary of your conclusion.

We reject H₀ and conclude that the intervention increased test scores.

We do not reject H₀ and conclude that the intervention had no significant effect on test scores.    

(e) Find a 95% confidence interval for the difference between the two means. Compare the information given by the interval with the information given by the significance test. (Round your answer to two decimal places

(f) The women in this study were all residents of Durham, North Carolina. To what extent do you think the results can be generalized to other populations?

The results for this sample will generalize well to all other areas of the country.

The results for this sample may not generalize well to other areas of the country.    

Answer 1

(a) The distribution is Normal because the sample sizes are large.

--------------------------------

(b)

The t procedures should be appropriate because we have two large samples with no outliers.

(c)

The one-sided alternative reflects the researchers' (presumed) belief that the intervention would increase scores on the test. The two-sided alternative allows for the possibility that the intervention might have had a negative effect.

Hypotheses are:

H0: μIntervention = μ2; Ha: μIntervention > μControl

(d)

t = 7.018

df = 378

p-value = 0.0000

We reject H0 and conclude that the intervention increased test scores.

(e)

Answer: (0.83, 0.85)

Since confidence interval does not contain zero so we reject the null hypothesis.

(f)

The results for this sample may not generalize well to other areas of the country.