A random sample of 40 hotel reviews is drawn from a large population of hotel customers. Give the standard deviation of the hotel's star rating.

Question

A random sample of 40 hotel reviews is drawn from a large population of hotel customers. It's known that 30% of the population left the hotel 1 star, 20% left 2 stars, 20% left 3 stars, and 30% left 4 stars. Give the standard deviation of the hotel's star rating.

The choices are:

0.1891

0.1893

0.1904

0.1934

Answer 1

The standard deviation of the 40 hotels ratings, scored as 1, 2, 3, or 4 depends on the mean of the 40 ratings.

The mean of the 40 ratings is 2.5 stars. The population standard deviation sigma = 1.2042.

I think what you were interested in is finding the population standard ERROR, which is sigma/sqrt(n).

This is 1.2042 / sqrt(40) = 0.1904 which is choice c.