Consider the hypotheses shown below. Given that x-110, = 26, n = 43, -0.01, comp
ID: 3322520 • Letter: C
Question
Consider the hypotheses shown below. Given that x-110, = 26, n = 43, -0.01, complete parts a through c below. Hu: = 117 HA : #117 a. State the decision rule in terns of the critical value(s) of the test statistic Reject the null hypothesis if the calculated value of the test statistic, z, is not contained within the critical value(s),. Otherwise, do not reject the null hypothesis Round to two decimal places as needed. Use a comma to separate answers as needed.) b. State the calculated value of the test statistic. The test statistic is Round to two decimal places as needed.) c. State the conclusion. Because the test statisti the null hypothesis and conclude the population mean equal to 117.Explanation / Answer
Given :- sample mean is X¯=110 and the known population standard deviation is =26, and the sample size is n=43.
(1) Null and Alternative Hypotheses
The following null and alternative hypotheses need to be tested:
Ho: =117
Ha: 117
This corresponds to a two-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
(2) Rejection Region
Based on the information provided, the significance level is =0.01, and the critical value for a two-tailed test is zc=2.58.
The rejection region for this two-tailed test is R={z:|z|>2.58}
(3) Test Statistics
The z-statistic is computed as follows:
z=[ (X¯–0) / (/n) ] = [ (110–117) / (26/43) ] = -1.76
(4) Decision about the null hypothesis
Since it is observed that |z|=1.76 zc=2.58, it is then concluded that the null hypothesis is not rejected and conclude the population mean is equal to 117.
Using the P-value approach: The p-value is p=0.0775, and since p=0.07750.01, it is concluded that the null hypothesis is not rejected.
(5) Conclusion
It is concluded that the null hypothesis Ho is not rejected. Therefore, there is not enough evidence to claim that the population mean is different than 117, at the 0.01 significance level.