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)

df = n - 1 = 26 - 1 = 25

From T table,

t critical value at 0.10 significance level with 25 df = 1.708

90% confidence interval for is

- t * S / sqrt(n) < < + t * S / sqrt(n)

348 - 1.708 * 22 / sqrt(26) < < 348 + 1.708 * 22 / sqrt(26)

340.63 < < 355.37

90% CI Is ( 340.63 , 355.37 )

b)

Interpretation = We are 90% confident that the average number of songs college students have

on their playlist is between 340.63 and 355.37

c)

We asuume that distribution is normally distributed.