Question

You wish to test the claim that mu equals880 at a level of significance of alpha equals0.01 and are given sample statistics n equals 35 and x overbar equals 850. Assume the population standard deviation is 82. Compute the value of the standardized test statistic. Round your answer to two decimal places. You wish to test the claim that mu equals880 at a level of significance of alpha equals0.01 and are given sample statistics n equals 35 and x overbar equals 850. Assume the population standard deviation is 82. Compute the value of the standardized test statistic. Round your answer to two decimal places.

Answer 1

Solution :

Given that,

Population mean = = 880

Sample mean = = 850

Population standard deviation = = 82

Sample size = n = 35

Level of significance = = 0.01

This is a two tailed test.

The null and alternative hypothesis is,

Ho: 880

Ha: 880

The test statistics,

Z =( - )/ (/n)

= ( 850 - 880 ) / ( 82 / 35)

= -2.16

Critical value of  the significance level is α = 0.01, and the critical value for a two-tailed test is

= 2.58

Since it is observed that |z| = 2.16 = 2.58 , it is then concluded that the null hypothesis is fails to reject.

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

= 2 * P(Z < -2.16)

= 2 * 0.0154

= 0.0308

The p-value is p = 0.0308, and since p = 0.0308 0.01 , it is concluded that the null hypothesis is fails to reject.

Conclusion :

It is concluded that the null hypothesis Ho is fails to reject. Therefore, there is not enough evidence to claim that the population mean μ is different than 880, at the 0.01 significance level.