Question

According to a magazine, people read an average of more than three books in a month. A survey of 30 random individuals found that the mean number of books they read was 3.2 with a standard deviation of 1.25. a. To test the magazine's claim, what should the appropriate hypotheses be? b. Compute the test statistic. c. Using a level of significance of 0.05, what is the critical value? d. Find the p-value for the test. e. What is your conclusion?

Answer 1

Solution :

$\mu$= 3

$\bar x$ = 3.2

s =1.25

n = 30

a ) This is the right tailed test .

The null and alternative hypothesis is ,

H₀ :  $\mu$  = 3

H_a : $\mu$ > 3

b ) Test statistic = t

= ($\bar x$ - $\mu$ ) / s / $\sqrt$ n

= (3.2 - 3) / 1.25 / $\sqrt$ 30

= 0.876

Test statistic = t = 0.876

P-value =0.1940

c ) The significance level is α =0.05, and the critical value for a right-tailed test is tc​ =1.699

d ) P-value ≥ $\alpha$

0.1940 ≥ 0.05

e )The null hypothesis Ho is not rejected.

Therefore, there is not enough evidence to claim that the population mean μ is greater than 3, at the 0.05 significance level.