Question

Consider the hypotheses shown below. Given that x overbarequals110​, sigmaequals27​, nequals44​, alphaequals0.10​, complete parts a and b. Upper H 0​: muequals118 Upper H 1​: munot equals118 ​a) What conclusion should be​ drawn? ​b) Determine the​ p-value for this test.

​a) The​ z-test statistic is?

b) p value is?

Answer 1

Solution :

Given that,

Population mean = = 118

Sample mean = = 110

Population standard deviation = = 27

Sample size = n = 44

Level of significance = = 0.10

This is a two tailed test.

The test statistics,

Z =( - )/ (/n)

= ( 110 - 118 ) / ( 27 / 44 )

= -1.97

P- Value = 2*P(Z < z )

= 2*P( Z < -1.97)

= 2*0.0244

= 0.0488

The p-value is p = 0.0488, and since p = 0.0488 < 0.10, it is concluded that the null hypothesis is rejected.

Conclusion :

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population

mean μ is different than 118, at the 0.10 significance level.