A dietician obtained a sample of 120 sixth-grade boys who followed a primarily v

Question

A dietician obtained a sample of 120 sixth-grade boys who followed a primarily vegetarian diet. She found their average weight to be 79 pounds. She wondered if the boys on the vegetarian diet weighed less than the typical sixth-grade boys, who average a weight of 85 pounds with a standard deviation of 12. Complete the six steps of hypothesis testing to investigate whether sixth-grade boys on the vegetarian diet weigh less than the general population of sixth-grade boys.

Label each step and follow the format presented in class. Assume alpha level = .05

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H0   H1    ±      

Explanation / Answer

sample mean is X¯=85 and the known population standard deviation is =12, and the sample size is n=120.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: 79

Ha: <79

This corresponds to a left-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 =0.05, and the critical value for a left-tailed test is zc=1.64.

The rejection region for this left-tailed test is R ={z:z<1.64}

(3) Test Statistics

The z-statistic is computed as follows:

z= (X¯0) / (/n ) = (85 - 79) / (12/120) = 5.477

(4) Decision about the null hypothesis

Since it is observed that z=5.477 zc=1.64, it is then concluded that the null hypothesis is not rejected.

P-value : The p-value is p=1, and since p=1 0.05, 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 less than 79, at the 0.05 significance level.

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