Question

#14) A researcher collected data on the eating habits of 64 Americans in 2018 and finds that they eat an average of 125 lbs of cheese per year with a sample standard deviation of 40 lbs.

a) Can we definitively say that Americans eat more than 120 lbs of cheese per year? Show all steps of the hypothesis test to test this question. (15pts)

b) Find the 95% confidence interval for cheese an average American consumes per year. (5pts)

Answer 1

The provided sample mean is and the sample standard deviation is s=40, and the sample size is n = 64

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho: μ = 120

Ha: μ > 120

This corresponds to a right-tailed test, for which a t-test for one mean, with unknown population standard deviation will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the critical value for a right-tailed test is tc​=1.669.

The rejection region for this right-tailed test is R=t:t>1.669

(3) Test Statistics

The t-statistic is computed as follows:

(4) The decision about the null hypothesis

Since it is observed that t=1≤tc​=1.669, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p=0.1606, and since p=0.1606≥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 μ is greater than 120, at the 0.05 significance level.

Graphically

b)

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