Question

Question 6: In the following: a). Identify the claim and state H0 and Ha. b). Find critical value(s) and the rejection region(s). c). Find the standardized test statistic: t-score. d). Decide whether to reject or fail to reject null hypothesis. e). Interpret the decision in context of original claim. A magazine claims that the mean amount spent by a customer at Burger Stop is greater than the mean amount spent by a customer at Fry world. The results are given below. At α = 0.05 can you support the magazines claim? Assume the population variances are equal. Burger Stop Fry World x1 = 5.46$ x2 = 5.12$ s1 = 0.89$ s2 = 0.79$ n1 = 22 n2 = 30

Answer 1

The provided sample means are shown below:

Also, the provided sample standard deviations are:

and the sample sizes are n1​=22 and n2​=30.

(1) Null and Alternative Hypotheses

The following null and alternative hypotheses need to be tested:

This corresponds to a right-tailed test, for which a t-test for two population means, with two independent samples, with unknown population standard deviations will be used.

(2) Rejection Region

Based on the information provided, the significance level is α=0.05, and the degrees of freedom are df = 50 . In fact, the degrees of freedom are computed as follows, assuming that the population variances are equal:

Hence, it is found that the critical value for this right-tailed test is t_c = 1.676, for α=0.05 and df = 50.

(3) Test Statistics

Since it is assumed that the population variances are equal, the t-statistic is computed as follows:

(4) Decision about the null hypothesis

Since it is observed that t = 1.453 ≤tc​=1.676, it is then concluded that the null hypothesis is not rejected.

Using the P-value approach: The p-value is p = 0.0762 , and since p = 0.0762 ≥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 μ1​ is greater than μ2​, at the 0.05 significance level.

Hence, the mean amount spent by a customer at Burger Stop is equal to the mean amount spent by a customer at Fry world