For the following hypothesis test: With n = 80,σ = 9,and = 47.1,state the decision rule in terms of the critical value of the test statistic.
A)Reject the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,1.645.Otherwise,do not reject.
B)Reject the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,2.05.Otherwise,do not reject.
C)Accept the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,1.645.Otherwise,do not accept.
D)Accept the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,2.05.Otherwise,do not accept.

Question

For the following hypothesis test:  With n = 80,σ = 9,and  = 47.1,state the decision rule in terms of the critical value of the test statistic.
A)Reject the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,1.645.Otherwise,do not reject. 
B)Reject the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,2.05.Otherwise,do not reject. 
C)Accept the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,1.645.Otherwise,do not accept. 
D)Accept the null hypothesis if the calculated value of the test statistic,z,is greater than the critical value of the test statistic,2.05.Otherwise,do not accept.

Quizplus · Accepted Answer

Since the population standard deviation (σ) is known, we can use a z-test. The null hypothesis is not given, so we cannot determine the direction of the test. Therefore, we will use a two-tailed test. 
The critical value of the test statistic is found using the standard normal distribution table, at the significance level of 0.05/2 = 0.025 (since it's a two-tailed test). The corresponding z-value is 2.05. Therefore, we reject the null hypothesis if the calculated value of the test statistic, z, is greater than 2.05 or less than -2.05. If the calculated value of z falls within the range between -2.05 and 2.05, we do not reject the null hypothesis.

For the Following Hypothesis Test: with N = 80,σ