Question

A random sample of 100 observations from a population with standard deviation 22.99 yielded a sample mean of 94.1. 1. Given that the null hypothesis is μ≤90 and the alternative hypothesis is μ>90 using α=.05, find the following: (a) Test statistic = (b) P - value: (c) The decision for this test is: A. Fail to reject the null hypothesis B. Reject the null hypothesis C. None of the above 2. Given that the null hypothesis is μ=90 and the alternative hypothesis is μ≠90 using α=.05, find the following: (a) Test statistic = (b) P - value:

Answer 1

1)

Solution :

Given that,

= 94.1

= 90

= 22.99and

n = 100

(a)

Test statistic = z = ( - ) / / n = (94.1 - 90) / 22.99 / 100 = 1.78

This is the right tailed test .

(b)

P(z > 1.78) = 1 - P(z < 1.78) = 1 - 0.9625 = 0.0375

P-value = 0.0375

(c) = 0.05

P-value < 0.05

B) Reject the null hypothesis .

2)

Test statistic = z = ( - ) / / n = (94.1 - 90) / 22.99 / 100 = 1.78

This is the two tailed test .

P(z > 1.78) = 1 - P(z < 1.78) = 1 - 0.9625 = 0.0375

P-value = P(z > 1.78) * 2 = 0.075