Question

(Round all intermediate calculations to at least 4 decimal places.) Consider the following hypotheses: H0: μ ≥ 177 HA: μ < 177 A sample of 84 observations results in a sample mean of 170. The population standard deviation is known to be 24. Use Table 1. a. What is the critical value for the test with α = 0.05 and with α = 0.01? (Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.) Critical Value α = 0.05 α = 0.01 b-1. Calculate the value of the test statistic. (Negative value should be indicated by a minus sign. Round your answer to 2 decimal places.) Test statistic b-2. Does the above sample evidence enable us to reject the null hypothesis at α = 0.05? Yes since the value of the test statistic is less than the negative critical value. No since the value of the test statistic is not less than the negative critical value. Yes since the value of the test statistic is not less than the negative critical value. No since the value of the test statistic is less than the negative critical value. c. Does the above sample evidence enable us to reject the null hypothesis at α = 0.01? Yes since the value of the test statistic is less than the negative critical value. No since the value of the test statistic is not less than the negative critical value. Yes since the value of the test statistic is not less than the negative critical value. No since the value of the test statistic is less than the negative critical value.

Answer 1

Consider the following hypotheses: H0: μ ≥ 177 HA: μ < 177

a. What is the critical value for the test with α = 0.05 and with α = 0.01?

The critical value of Z at 5% significance level is -1.645

The critical value of Z at 1% significance level is -2.33

b-1. Calculate the value of the test statistic.

Under H0, the test statistic is

b-2. Does the above sample evidence enable us to reject the null hypothesis at α = 0.05?

Yes since the value of the test statistic is less than the negative critical value.

c. Does the above sample evidence enable us to reject the null hypothesis at α = 0.01?

Yes since the value of the test statistic is less than the negative critical value.