Question

Theme park spending In a random sample of 40 visitors to a certain theme park, it was determined that the mean amount of money spent per person at the park (including ticket price) was $93.43 per day with a standard deviation of $15. Construct and interpret a 99% confidence interval for the mean amount spent daily per person at the theme park.

Answer 1

The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.

This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.

Explanation:

We have the sample standard deviation, 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 = 40 - 1 = 39

99% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 39 degrees of freedom(y-axis) and a confidence level of
`1 - (1 - 0.99)/(2) = 0.995`. So we have T = 2.7079

The margin of error is:

M = T*s = 2.7079*15 = 40.62

In which s is the standard deviation of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 93.43 - 40.62 = $52.81.

The upper end of the interval is the sample mean added to M. So it is 93.43 + 40.62 = $134.05

The 99% confidence interval for the mean amount spent daily per person at the theme park is between $52.81 and $134.05.

This means that we are 99% sure that the true mean amount spent daily per person at the theme park is between $52.81 and $134.05.