Question

#2. Researchers would like to know the mean body temperature of runners at the completion of a marathon. They plan to take a random sample of 100 runners who complete a marathon and record their temperatures. Choose the answers from the ---Select--- choice

- Need help with #2 (a-c) all related questions to the given information

-Please choose/ answer the correct based on (---Select---) answers

-It is a different solution from the original solution statistic book

(a) the value of the mean of the sampling distribution of the sample mean The mean of the sampling distribution is based on the population mean and thus would ---Select--- (1. be known only after/ 2. not be known even after/ 3. be known even before) taking the sample.

(b) the approximate shape of the sampling distribution of the sample mean The approximate shape is normal and thus would ---Select--- (1.be known only after/ 2. not be known even after/ 3. be known even before) taking the sample.

(c) the standard deviation of the sampling distribution of the sample mean The standard deviation of the sampling distribution is ---Select--- (1. based on the sample mean/ 2. based on the population standard deviation/ 3. based on the sample standard deviation/ 4. based on the population mean) and thus would ---Select--- (1. be known only after/ 2. not be known even after/ 3. be known even before) taking the sample.

Answer 1

We know that-

If X follows Normal distribution with mean $\mu$ and standard deviation $\sigma$ , then the sample take from X having sample mean x bar has Normal distribution with mean $\mu$ and standard deviation $\sigma/\sqrt{n}$

Hence -

a) the value of the mean of the sampling distribution of the sample mean The mean of the sampling distribution is based on the population mean and thus would 3. be known even before taking the sample.

b) the approximate shape of the sampling distribution of the sample mean The approximate shape is normal and thus would 3. be known even before taking the sample.

(c) the standard deviation of the sampling distribution of the sample mean The standard deviation of the sampling distribution is  2. based on the population standard deviation and thus would 3. be known even before taking the sample.

Hope this will help you. Thank you :)