Question

The director of the Baton Rouge YMCA notes that, in past years, the average member has held a membership for a period of 2.7 years. He had implemented a marketing strategy and wants to determine if that campaign was effective in changing the average membership period. He takes a random sample of 40 members and finds that the average membership period is 3.35 years with a sample standard deviation of 1.5 years. In order to test the hypothesis H0: µ = 2.7 versus H1: µ ≠ 2.7 at 0.01 level of significance, the critical value(s) is(are) ________________.

Select one:

± 2.708

2.708

2.426

± 2.575

± 1.688

Answer 1

Solution :

The null and alternative hypothesis is ,

H0 :   = 2.7

Ha :    2.7

= 3.35

s = 1.5

n = 40

degrees of freedom = n - 1 = 40 - 1 = 39

This is the two tailed test,

= 0.01

/2 = 0.005

t/2,df = t0.005,39  ± 2.708

± 2.708