Question

Test the claim about the population​ mean, mu​, at the given level of significance using the given sample statistics. ​Claim: mu: 50​; alpha=0.03​; sigmaequals3.63. Sample​ statistics: x overbarequals48.7​, nequals69What are the critical values?

Answer 1

Solution :

Given that,

Population mean = = 50

Sample mean = = 48.7

Population standard deviation = = 3.63

Sample size = n = 69

Level of significance = = 0.03

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: 50

Ha: 50

Critical value

Based on the information provided, the significance level is α=0.03, and the critical value for a right-tailed test is

​=1.88.

The test statistics,

Z = ( - )/ (/)

=( 48.7 - 50 ) / ( 3.63 / 69)

= -2.975

Since it is observed that z = -2.975 ≤ ​=1.88, it is then concluded that the null hypothesis is fails to reject.