Question

In order to determine if there is any difference between the mean daily sales of 2 locations of an electronics chain, the data below has been gathered. At a 1% level of significance, test to determine if there is a significant difference in the mean daily sales of the 2 locations. What is your conclusion?

                                                           Center City Location     Suburban Mall Location

     Sample size                                               16                                         13

     Sample Mean                                          $36,500                           $38,000

     Sample Standard Deviation                   $3,000                             $4,200

Answer 1

ses The following null and alternative hypotheses need to be tested This corresponds to a two-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-0.01, and the degrees of freedom are df 27. 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 two-tailed test is tc 27 2.771, for a 0.01 and df - The rejection region for this two-tailed test is R = {t : 비 > 2.771} Since it is assumed that the population variances are equal, the t-statistic is computed as follows 1 36500 38000 = 1.121 13-1)4200 6-1 300 (4) Decision about the null hypothesis Since it is observed tha121 e 2.771, it is then concluded that the null hypothesis is not rejected Using the P-value approach: The p-value is p = 0.2721, and since p = 0.2721 > 0.01, 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 μι is different than μ-, at the 0.01 significance level The 99% confidence interval is 5207.12 < μ1-μ2 2207.12