Question

To test H0: mu=60 versus H1: mu<60, a random sample size n=25 is obtained from a population that is known to be normally distributed. Complete parts a through d below. a) if x bar= 57.4 and s= 14.1, compute the test statistic. b)If the researcher decides to test this hypothesis at the confidence variable= .1 level of significance, determine the critical value(s). c)draw the t-distribution that depicts the critical region. d)will the researcher reject the null hypothesis?

Answer 1

Solution :

a ) Given that,

= 60

=  57.4

s = 14.1

n = 25

This is the left tailed test .

The null and alternative hypothesis is ,

H₀ :   = 60

H_a : < 60

Test statistic = t

= ( - ) / s / n

= ( 57.4 - 60 ) / 14.1 / 25

= - 0.922

Test statistic = t = - 0.922

P-value = 0.1829

b ) = 0.1  

P-value ≥

0.1829 ≥ 0.1

c ) The significance level is α=0.1, and the critical value for a left-tailed test is tc ​=−1.318

d ) Not Reject the null hypothesis .

There is insufficient evidence to suggest that,