This project is designed to demonstrate some similarities and differences in what we learn about a parameter by constructing a confidence interval versus performing a hypothesis test.
It was estimated over a century ago that the average human body temperature was 98.6 F.
In recent years, scientists have begun to believe that the average human body temperature is closer to 97.5 ̊ F.
Let’s pretend our sample of 62 student temperatures is a simple random sample from the population of adults. (Remember it was a sample of convenience, not a simple random sample!) Use the sample mean of 98.01 ̊F and sample standard deviation of 0.72 degrees from our sample of 62 temperatures to construct a confidence interval and conduct a hypothesis test. (If you have trouble inserting the symbols, you may type “mu” and “xbar” in place of the appropriate symbol.)
1.
a) Using the sample data given, construct a 95% confidence interval for (population) mean body temperature. Show all calculations or include calculator functions/program and input used to find your answer. Round the confidence interval boundaries to one decimal place. Write your final answer as an inequality including the appropriate parameter.
b) Interpret the confidence interval.
c) Does our confidence interval support the scientists’ claim that the true mean body temperature for adults is less than 98.6 ̊ F? Using one or two sentences, fully explain your answer.
2.Using the sample data given and α=0.05, conduct a hypothesis test to test the claim that the mean body temperature of adults is less than 98.6 ̊ F. Show your work.
a.) State the null and alternate hypothesis
b.) What test will we use to conduct this hypothesis test? Fully justify your answer.
c.) Calculate the p value and test statistic. Round your answer to four decimal places.
d.) Draw the appropriate bell curve for this test. Label the region that corresponds to the p value.
e.) Do you reject or fail to reject the null hypothesis?
f.) Use a complete sentence to interpret the results.
3. Explain at least one similarity and at least one difference between what you concluded about from the confidence interval versus the hypothesis test.
Submit your Microsoft Excel File.
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