Please answer all questions.

DOES HEAT AFFECT COGNITIVE ABILITY?Forty-six college students at a college in the North-east were recruited to perform cognitive tasks every morning during a heat wave. Some of the students were in air-conditioned dorms and some were not. This exercise refers to one of the responses measured in the study.1The simplified data are available inHeatCognition. (While we only look at two responses here, it does appear in general that heat affects cognitive ability. On almost all the tasks, the students with air-conditioning performed better.)

1Cedeo Laurent JG, et al., "Reduced cognitive function during a heat wave among residents of non-air-conditioned buildings: An observational study of young adults in the summer of 2016."PLoS Med, 15(7): e1002605, July 10, 2018. Data is simplified from the repeated measures design used in the original study.

Does Heat Affect Math Reaction Time?One task asked students to add or subtract two-digit numbers as quickly as possible, with a z-score of their reaction time recorded inMathZRTinHeatCognition. Test to see if students with air-conditioning are faster at this task (with a smaller mean reaction time), on average, than students without. Let Group 1 represent students with air-conditioning and Group 2 represent those without, giving a left-tail test. Show all details: hypotheses, sample statistic, p-value, and conclusion in context.