Reconsider the previous two exercises. In this question, we will focus on comparing 10 males who…

Reconsider the previous two exercises. In this question, we
will focus on comparing 10 males who breathe only through their left nostril to
10 males who breathe only through their right nostril while they perform a
verbal task. Assume that the verbal scores in each group are fairly symmetric.

 a. When the average scores on the verbal task obtained by
the males in the study were compared using a two-sided alternative hypothesis
and two-sample t-test, the p-value turned out to be 0.0162. Use this p-value
and a 1% level of significance to state an appropriate conclusion in the
context of the study. Explain your reasoning.

 b. How, if at all, would your conclusion in part (a) change
if you were to use a 5% level of significance?

c. In the context of this study and the related data
results, which of the following statements are true?

 i. The 95% confidence interval for the difference in the
mean scores between males in the “population” who perform a verbal task while
breathing through only the left nostril versus only the right nostril will
contain 0 because the p-value is less than 5%.

 ii. The 95% confidence interval for the difference in the mean
scores between males in the “population” who perform a verbal task while
breathing through only the left nostril versus only the right nostril will not
contain 0 because the p-value is less than 5%.

 iii. The 99% confidence interval for the difference in the
mean scores between males in the “population” who perform a verbal task while
breathing through only the left nostril versus only the right nostril will
contain 0 because the p-value is greater than 1%.

 iv. The 99% confidence interval for the difference in the
mean scores between males in the “population” who perform a verbal task while
breathing through only the left nostril versus only the right nostril will not
contain 0 because the p-value is greater than 1%.

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