Question

1. Suppose the amount of money UCLA students spend on movies during a one month period observes normal distribution. A sample is taken containing monthly movie spending in dollars for several UCLA students as 66.72, 50.23, 40.57, 45.53, 60.45, 70.85, 57.49, and 53.46. Round your numbers to two decimal places. All the calculation should be preceded with the formula used.

b. Estimate the average monthly movie spending by all UCLA students with a 95% confidence interval.

Answer 1

The computations would be made from the following table here:

X	(X - Mean(X))^2
66.72	122.2683063
50.23	29.51205625
40.57	227.7835563
45.53	102.6675563
60.45	22.92015625
70.85	230.6601563
57.49	3.33975625
53.46	4.85100625
445.3	744.00255

The sample mean and sample standard deviation here are computed as:

For n - 1 = 7 degrees of freedom, we have from t distribution tables here:

P( t₇ < 2.365) = 0.975

Therefore, P( - 2.365 < t₇ < 2.365) = 0.95

Therefore the confidence interval for population mean here is obtained as:

This is the required 95% confidence interval here.