Question

A recent national survey found that parents read an average (mean) of 10 books per month to their children under five years old. The population standard deviation is 5. The distribution of books read per month follows the normal distribution. A random sample of 25 households revealed that the mean number of books read last month was 12. At the .01 significance level, can we conclude that parents read more than the average number of books to their children?

What is the probability of a Type II error? (Round your answer to 4 decimal places.)

Answer 1

Hence, We cannot conclude that parents read more than the average number of books to their children at 0.01 significance level.

Now,

We will fail to reject null hypothesis when we get Z-statistics less than or equal to 1.645 ( Value of Z at 0.05 level of significance)

We need to find :

such that :

Probability of Type II error is :

Using Excel function "NORMSDIST()" to find the above probability as :

Hence,

Probability of Type II error = 0.3613