Reconsider the previous exercise. In this question, we will focus on comparing 10 males who were randomly assigned to breathe only through their left nostril to 10 who were randomly assigned to breathe only through their right nostril while they took the spatial and verbal tests. Note: Ten of the 30 total males were not assigned to either condition considered here. Here are the summary statistics on the spatial test performance; the data are fairly symmetric in both groups.

a. Describe the parameter(s) of interest in the context of this study.
b. State the null and the alternative hypotheses (two-sided test) in the context of the study.
c. Name the appropriate theory-based method you would use to test the hypotheses stated in part (b).
d. State the validity conditions that have to be met to be able to perform the test named in part (c). Are these conditions met? How are you deciding?
e. Regardless of your answer to part (d), perform the theory-based test proposed in part (c). Be sure to include a test statistic value and a p-value in your answer.
f. Based on your p-value, state your conclusion in the context of the study. Be sure to comment on statistical significance, 95% confidence interval, causation, and generalization.
g. Without performing any additional calculations, explain how, if at all, the p-value reported in part (f) would change if each condition was implemented on 30 males in each group instead of 10 males in each group but the means and SDs stayed the same.
h. Without performing any additional calculations, explain how, if at all, the p-value reported in part (f) would change if the mean for €œleft € condition was 10.9 and that for €œright€ was 13.4 but the sample sizes and SDs stayed the same.
i. Without performing any additional calculations, explain how, if at all, the p-value reported in part (f) would change if SDs for both conditions were 2.00 but the sample sizes and means stayed the same.

Data from previous question

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.

Transcribed Image Text:

Spatial test Mean Condition SD Left nostril breathing 8.90 2.80 Right nostril breathing 2.00 11.40 Spatial Verbal Sex Mean SD Mean SD Male 2.70 10.90 3.00 10.20 Female 2.50 15.10 3.40 7.80