3. A diet clinic states that there is an average loss of 24 pounds for those who stay on the program for 20 weeks. The standard deviation is 5 pounds. The clinic tries a new diet, reducing salt intake to see whether that strategy will produce a greater weight loss. A group of 40 volunteers loses as as average of 16.3 pounds each over 20 weeks. Should the clinic change the new diet? Use a 0.05
The following null and alternative hypotheses need to be tested:
This corresponds to a right-tailed test, for which a z-test for one mean, with known population standard deviation will be used.
Based on the information provided, the significance level is and the critical value for a right-tailed test is
The rejection region for this right-tailed test is
The z-statistic is computed as follows:
6. Since it is observed that it is then concluded that the null hypothesis is not rejected.
Using the P-value approach:
The p-value for right-tailed is and since it is concluded that the null hypothesis is not rejected.
Therefore, there is not enough evidence to claim that the population mean
is greater than 24, at the significance level.
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