The sample mean sample standard deviation and sample size we

The sample mean, sample standard deviation, and sample size were given. Use the one-mean t-test to perform the required hypothesis test about the mean, m, of the population from which the sample is drawn. Use the critical value approach. x=137

s=14.2

n=20

H0: m=132

Ha: M (does not =) 132

a=0.1

Solution

s=14.2

n=20

H0: m=132

Ha: M (does not =) 132

a=0.1

the test statistic is t = (137-132)/(14.2/sqrt 20) = 1.575

to find the critical values, look up on the t distribution table, alpha/2 = .1/2 = .05 (divide alpha by 2 since this is a not equal or 2-tailed test) and df = 20-1 = 19.

So look under the .05 column and the row where df = 19, the t score is 1.729.

So the critical values are +1.729 and -1.729.

Since the test statistic, t = 1.575 is neither greater than 1.729 nor less than -1.729, we fail to reject the null hypothesis.

Conclusion: There is not enough evidence at the .1 level of significance that the mean does not equal 132.