Question

John is interested in studying the amount of books a person reads in a year. He found out that in 2017 U.S. citizens read an average of 12 books with a standard deviation of 4. John wants to know if he reads significantly more books and counted the number of books that he read last year. In 2017, John read 16 books. Did John read significantly more books? a. What is the correct test for this question? b. What are the hypotheses? c. Calculate the degrees of freedom. d. What is the cutoff(s)? e. Test the hypotheses. Calculate the score (use equation from chart) then compare to the cutoff. f. What type of error could have been made? What would it state?

Answer 1

The mean and population standard deviation for the number of books U.S citizens read in 2017 is

a) Now since the population standard deviation is given we will use Z test for one mean.

b) We have to test if on average John read more books.

Null hypothesis:

alternate hypothesis:

c) We will not calculate the degree of freedom as it is a Z test for mean.

d) For significance level:

and this is the one-tailed test - right-tailed test.

he critical Z value is

We will reject the null if we get a Z statistic greater than 1.645

The cutoff is 1.645

e-f) the test. statistic:

Since the test statistic is less than the cutoff value we fail to reject the null hypothesis.

g) Since we have failed to reject the null hypothesis, and if the null hypothesis is false we might have committed the type II error.