3 Body Temperature It has long been asserted that the average body temperature was 98.6 degrees Fahrenheit. A 1992 study aimed to test this hypothesis. (The data presented here is fictionalized but similar to the study data.) The body temperatures of a sample of 130 adults were taken to one decimal place. The mean temperature of the sample was 98.5 degrees, the median was 98.3 degrees, and the standard deviation was 0.73 degrees. The figures below show a histogram of the data and a normal quantile plot of the data. Histogram of Temperature Normal Q-Q Plot 8 15 20 Sample Quantles Frequency 5 10 97 100 101 Temperature 1. (2 points) From the information provided, does it seem like the distribution of body temper- atures is (i) exactly normal, (ii) approximately normal, or (iii) not close to normal? Explain your choice. 2. (4 points) Let / be the population mean body temperature (not the median!) We wish to test Ho : / = 98.6 against H1 : / =98.6. Assuming this is a random sample, calculate a test statistic and give R code for the P-value of this test. (Only use R. code for the P-value!) 3. (4 points) Construct an approximate 95% confidence interval for the population mean body temperature. (Show how you calculate it and give a numerical answer - apply the Central Limit Theorem if necessary.) Summarize the evidence for or against the null hypothesis