Question

Consider the following hypothesis test:

H ₀:   50

H _a:  > 50

A sample of 50 is used and the population standard deviation is 7. Use the critical value approach to state your conclusion for each of the following sample results. Use  = .05.

a. With x (with line over top of x) = 52.5, what is the value of the test statistic (to 2 decimals)?

b. With x = 51, what is the value of the test statistic (to 2 decimals)?

c. With x = 51.8, what is the value of the test statistic (to 2 decimals)?

Answer 1

For the given hypotheses:

Ho: =   50

Ha:   > 50

Based on the hypothesis it will be a right-tailed test.

Rejection region:

At 0.05 level of significance and using the excel formula for normal distribution the critical Z score is calculated as =NORM.S.INV(0.95), thus the Zc computed as 1.645.

So, reject Ho if Z is greater than Zc.

a) If a sample of n = 50 is used and the standard deviation used is = 7, the test statistic is calculated as:

Conclusion:

Since Z > Zc hence we reject the null hypothesis and conclude that there is enough evidence to support the claim.

b) At Sample mean = 51 the test statistic is calculated as:

Conclusion:

Since Z < Zc hence we cannot reject the null hypothesis and conclude that there is insufficient evidence to support the claim.

c) With sample mean = 51.8

Conclusion:

Since again Z <Zc hence we cannot reject the null hypothesis and conclude that there is insufficient evidence to support the claim.