Question

A group of 49 randomly selected construction workers has a mean age of 22.4 years with
a standard deviation of 3.8. According to a recent survey, the mean age should be μ =
21.9 years. Test this hypothesis at the 0.02 level of significance to determine if there is
enough evidence to support the claim..
?0 = ___________________________________
?? = ___________________________________
Test Statistic = __________________________
Alpha (?) level of significance= __________________
Classical Critical Value = ____________________
?-value = _______________________________
________Conclusion: A) reject ?0 B) fail to reject ?0
________Interpretation:
A) There is sufficient evidence to support the claim.
B) There is insufficient evidence to support the claim.

Answer 1

Solution :

This is the two tailed test .

The null and alternative hypothesis is ,

H₀ :   = 22.4

H_a :    22.4

Test statistic = z

= ( - ) / / n

= (21.9 - 22.4) / 3.8 / 49

= -0.92

Level of significance = = 0.02

/ 2 = 0.02 / 2 = 0.01

Z_/2 = Z _0.01 = 2.326

Critical value = -2.326 , +2.326

P(z < -0.92) = 0.1788

P-value = 0.3576

= 0.02

P-value >

Fail to reject the null hypothesis .

B) There is insufficient evidence to support the claim.