Self-efficacy is a general concept that measures how well we think we can contro
ID: 3063244 • Letter: S
Question
Self-efficacy is a general concept that measures how well we think we can control different situations. 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. Participants were asked, "How sure are you that you can eat foods low in fat over the next month?" The response was measured on a five-point scale with 1 corresponding to "not sure at all" and 5 corresponding to "very sure." Here is a summary of the self-efficacy scores obtained about 2 months after the intervention:
x
(a) Do you think that these data are Normally distributed? Explain why or why not.
The distribution is not Normal because all scores are integers.
The distribution is Normal because the sample sizes are large.
The distribution is not Normal because the sample included only women.
The distribution is Normal because the standard deviation is smaller than the mean.
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 Normally distributed data.
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.
(c) Describe appropriate null and alternative hypotheses.
H0: Intervention 2; Ha: Intervention < Control (or Intervention = Control)
H0: Intervention = 2; Ha: Intervention > Control (or Intervention < Control)
H0: Intervention 2; Ha: Intervention > Control (or Intervention = Control)
H0: Intervention = 2; Ha: Intervention > Control (or Intervention = Control)
H0: Intervention = 2; Ha: Intervention < Control (or Intervention 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 decrease scores on the test. The two-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 decrease scores on the test. The one-sided alternative allows for the possibility that the intervention might have had a positive effect.
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 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 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.
(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.)
Write a short summary of your conclusion.
We do not reject H0 and conclude that the intervention had no significant effect on test scores.
We reject H0 and conclude that the intervention increased 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
(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 may not generalize well to other areas of the country.
The results for this sample will generalize well to all other areas of the country.
Group nx
s Intervention 168 4.11 1.19 Control 213 3.62 1.12Explanation / Answer
a)
The distribution is normal because the sample size is large.
b)
The t procedures should be appropriate because we have Normally distributed data.
c)
The appropriate null and alternative hypothesis is
H0: Intervention 2; Ha: Intervention > Control (or Intervention = Control)
d)
Intermediate values used in calculations:
t = 4.1244
df = 379
standard error of difference = 0.119
P value and statistical significance:
The two-tailed P value is less than 0.0001
By conventional criteria, this difference is considered to be extremely statistically significant.
We reject H0 and conclude that the intervention increased test scores.
e)
Confidence interval:
The mean of Group One minus Group Two equals 0.4900
95% confidence interval of this difference: From 0.2564 to 0.7236
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