Question

A researcher decides to study if having a pet leads to lower levels of anxiety. She collects data from a sample of dog owners (n=30) and measures their anxiety levels, which range between 0 and 100. She finds a mean level of anxiety of 68 with a standard deviation of 5. This researcher knows that the mean anxiety level of the population is 60, and wants to compare it to this sample.

Calculate the 95% confidence interval for this test (One-Sample t-Test).

Answer 1

To find the 95% CI for the mean anxiety level of the population.

Let be the sample mean

Given

95% CI is given by

where t is the table value from t distribution table with (n-1)=29 degrees of freedom

Hence the above is the 95% CI for the population mean of anxiety level.

Thank you !!