Question

A budding statistician wants to determine the average number of songs college students
have on their playlist. They take a random sample of 26 students at their university and find the
sample mean is 348 songs with a sample standard deviation of 22 songs.

a. Find a 90% confidence interval for the mean number of songs college students have on their
playlist.

b. Interpret the confidence interval you found in part a.

c. State the assumptions needed for your confidence interval to be valid.

Answer 1

a. 90% confidence interval for the mean number of songs college students have on their playlist is (310,386)

b. Were this procedure to be repeated on numerous samples, the fraction of calculated confidence intervals (which would differ for each sample) that encompass the true population parameter would tend toward 90%.

c. The assumption for this confidence interval to be valid is that population should be a normal distribution