Question

For a normally distributed population, :

An article claims the mean weight of 50-year-old men is greater than or equal to 185 lbs. Stu is a researcher and he decides to sample the population. He obtains the weights of 40 50-year-old males and finds the mean weight to be 180 lbs.

Determine the test statistic that Stu should use to help make decisions about whether or not the mean weight is at least 185 lbs with 90% confidence.

Answer 1

Let X be the weight of 50 year old men (in lbs).

A researcher want to test whether the mean weight is at least 185 lbs at 10% level of significance.

A sample of 40, 50 year old males is taken and find the mean weight to be 180 lbs.

The test statistic should used to help make decision about whether or not the mean weight is at least 185 lbs is

t statistic.

Since the population standard deviation is not known we use t statistic.

The sample standard deviation is obtained from the sample.