Question

A random sample of 100100 observations from a population with standard deviation 12.6312.63 yielded a sample mean of 92.392.3.

1. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ>90μ>90 using α=.05α=.05, find the following:
(a) Test statistic ==
(b) P - value:
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

2. Given that the null hypothesis is μ=90μ=90 and the alternative hypothesis is μ≠90μ≠90 using α=.05α=.05, find the following:
(a) Test statistic ==
(b) P - value:
(c) The conclusion for this test is:

A. Reject the null hypothesis
B. There is insufficient evidence to reject the null hypothesis
C. None of the above

Answer 1

Solution :

Given that,

= 92.3

= 12.63

n = 100

(1)

= 90

Test statistic = z = ( - ) / / n

= (92.3 - 90) / 12.63 / 100 = 1.82

Test statistic = 1.82

This is the right tailed test .

P(z > 1.82) = 1 - P(z < 1.82) = 1 - 0.9656 = 0.0344

P-value = 0.0344

= 0.05

P-value <

Reject the null hypothesis .

(2)

= 90

Test statistic = z = ( - ) / / n

= (92.3 - 90) / 12.63 / 100 = 1.82

Test statistic = 1.82

This is the two tailed test .

P(z > 1.82) = 1 - P(z < 1.82) = 1 - 0.9656 = 0.0344

P-value = 2 * P(z > 1.82) = 2 * 0.0344 = 0.0688

P-value = 0.0688

= 0.05

P-value >

Fail to teject the null hypothesis .

There is insufficient evidence to reject the null hypothesis .