Question

In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $109.33 per class and the sample standard deviation of the amount spent per owner was $12. Construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class. Group of answer choices

Answer 1

The 95% confidence interval for the mean amount spent per owner for an obedience class is between $106.23 and $112.43. This means that we are 95% sure that the mean amount spent of all dog owners for the obedience class is between $106.23 and $112.43.

Explanation:

We have the standard deviation for the sample, so we use the t-distribution to solve this question.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 60 - 1 = 59

95% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 59 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.95)/(2) = 0.975`. So we have T = 2

The margin of error is:

`M = T(s)/(√(n)) = 2(12)/(√(60)) = 3.1`

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 109.33 - 3.1 = $106.23

The upper end of the interval is the sample mean added to M. So it is 109.33 + 3.1 = $112.43

The 95% confidence interval for the mean amount spent per owner for an obedience class is between $106.23 and $112.43. This means that we are 95% sure that the mean amount spent of all dog owners for the obedience class is between $106.23 and $112.43.