Changing normal ~ During the mid-nineteenth century, a German physician named Carl Wunderlich used over a million human body temperature readings to establish a standard "normal" body temperature of 37 degrees Celsius (98.6 degrees Farhenheit). Over time, however, and especially more recently, lower body temperatures have been reported in healthy adults.In a time of pandemic illness where fever is a widely reported symptom, experts are advising changes to how we understand "normal" body temperature and what measurements should be considered signs of illness.To add to the ongoing research, Dr. Black and their associates have decided to gather some data for analysis. The group recruits a random sample of 11 healthy adults in a nearby urban area and obtains a mean body temperature reading of 36.74 degrees Celsius with a standard deviation of 0.52.Dr. Black wants to conduct a hypothesis test to determine if the mean body temperature reading for the population of healthy adults in their area is less than 37 degrees Celsius.Round all calculated values to 4 decimal places as appropriate.1. Which hypothesis test should Dr. Black use?A. 22 test of independence B. Randomization test for the difference of two population proportions C. 22 goodness of fit test D. Z test for one population proportion E. t test for a population mean

2. Which set of hypotheses should Dr. Black use to answer the research question?A. H0:<36.74H0:<36.74 vs. Ha:>36.74Ha:>36.74 B. H0:=37H0:=37 vs. Ha:>37Ha:>37 C. H0:=37H0:=37 vs. Ha:37Ha:37 D. H0:=37H0:=37 vs. Ha:<37Ha:<37

3. What conditions must be met for the hypothesis test to be valid? Select all that apply: A. The sample body temperature readings must be normally distributed. B. There must be at least 3 levels of body temperature readings. C. There must be an expected variation in the body temperature readings of at least 5 degrees Celsius. D. Dr. Black must be able to assume that the distribution of body temperature readings in healthy adults is normally distributed. E. The sample observations must be independent.

4. What is the test statistic? ? z t X^2 =

5. Dr. Black calculates a p-value of 0.0641. Which of the following are correct interpretations of the p-value? Select all that apply: A. A p-value of 0.0641 means that there is a 6.41% chance that the null model is a good fit for the observed data. B. A p-value of 0.0641 means we have some evidence against the null hypothesis. C. Under the null model, we would expect a sample mean of 36.74 or less approximately 6.41% of the time in repeated sampling. D. A p-value of 0.0641 means we have some evidence that the null hypothesis is true.

6. Calculate the effect size for Dr. Black's hypothesis test.d^=d^=

Dr. Green and Dr. Brown are interested in replicating Dr. Black's research in additional urban areas. They each gather data in their areas and conduct hypothesis tests using the same null and alternative hypotheses.Dr. Green obtains a sample size of 19 healthy adults, a p-value of 0.018 and an effect size of -0.61.Dr. Brown obtains a sample size of 51 healthy adults, a p-value of 0.0223 and an effect size of -0.22.

7. Dr. Green's results ? confirm conflict with Dr. Brown's results because the ? p-values effect sizes sample sizes are ? similar dissimilar .