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 €œpopulation€ 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 €œpopulation€ 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 €œpopulation€ 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 €œpopulation€ 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%.

Data from previous question

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.

In an article titled €œUnilateral Nostril Breathing Influences Lateralized Cognitive Performance€ that appeared in Brain and Cognition (1989), researchers Block et al. published results from an experiment involving assessments of spatial and verbal cognition when breathing through only the right versus left nostril. The subjects were 30 male and 30 female right-handed introductory psychology students who volunteered to participate in exchange for course credit. Initial testing on spatial and verbal tests revealed the following summary statistics. Note that the scores on the spatial task can range from 0 to 40, whereas those on the verbal task can go from 0 to 20. The distributions are not strongly skewed on either scale or for males or females.

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Verbal Spatial Sex Mean SD Mean SD Male 2.70 10.90 3.00 10.20 Female 2.50 15.10 3.40 7.80