Question

An executive member of an ice cream company claimed that its product contained more than 500 calories per pint. To test this claim, 121 containers were randomly chosen and analyzed. The sample result showed that the mean was 506 calories with standard deviation of 33 calories. (a) At α= 5%, using the classical approach to test the claim. (2)Using P-value approach to conclude it.

Answer 1

The provided sample mean is and the sample standard deviation is s = 33, and the sample size is n=121.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

Ho:

Ha:

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​=1.658.

The rejection region for this right-tailed test is R=t:t>1.658

(3) Test Statistics

The t-statistic is computed as follows:

(4) Decision about the null hypothesis

(a) Classical approach

Since it is observed that t=2>tc​=1.658, it is then concluded that the null hypothesis is rejected.

(b)

Using the P-value approach: The p-value is p=0.0239, and since p=0.0239<0.05, it is concluded that the null hypothesis is rejected.

(5) Conclusion

It is concluded that the null hypothesis Ho is rejected. Therefore, there is enough evidence to claim that the population mean μ is greater than 500, at the 0.05 significance level.

Graphically

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