Question

a random sample of 100 observations from a population. with standard deviation 60 yielded a sample mean of 110. A. test the null hypothesis that m = 100 and the alternative hypothesis m > 100 using alpha = .05 and interpret the results b. test the null against the alternative hypothesis that m isn't equal to 110. using alpha = .05 and interpret the results c. compare the p values of the two tests you conducted. Explain why the results differ.

Answer 1

Solution:

Part a

Here, we have to use one sample z test for population mean.

H₀: µ = 100 versus H_a: µ > 100

This is an upper tailed test.

α = 0.05

We are given

Xbar = 110

σ = 60

n = 100

Test statistic = Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (110 – 100)/[60/sqrt(100)]

Z = 10/6

Z = 1.6667

P-value = 0.0478

(by using z-table)

P-value < α = 0.05

So, we reject the null hypothesis

Part b

Here, we have to use one sample z test for population mean.

H₀: µ = 100 versus H_a: µ ≠ 100

This is an upper tailed test.

α = 0.05

We are given

Xbar = 110

σ = 60

n = 100

Test statistic = Z = (Xbar - µ)/[σ/sqrt(n)]

Z = (110 – 100)/[60/sqrt(100)]

Z = 10/6

Z = 1.6667

P-value = 0.0956

(by using z-table)

P-value > α = 0.05

So, we do not reject the null hypothesis

Part c

The p-value in the part b is twice or double of the p-value in the part a. In part a, we perform one tailed test while in part b we perform two tailed test. So, for second part, the p-value is double of part a.