Question

14.) A radical consumer group believes that the government is using mind controlom the general population with additives in the popular soft drink Pepsi. To test this conspiracy theory, the consumer group randomly selected 36 cans of Coke and so canso Hepsi to test if there is a difference in the mean weights as the additives while tasteless, are heavier than water). Test that the mean weight of Coloe is different from the mean weight of Pepsi using the given information. Keep 3 decimal places for the final value of the test statistic. Q-0.01 +10 than water diference in mly selec final valu weight of Coke Pepsi ni - 36 n - 36 61 -0.007507 X; -.81682 S2 - 0.005701 X 82410 Conclusion:

Answer 1

1= coke

2=pepsi

(1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: Mi = 112 Ha: Hi12 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 a = 0.01, and the degrees of freedom are df = 65.294. In fact, the degrees of freedom are computed as follows, assuming that the population variances are unequal: Hence, it is found that the critical value for this two-tailed test is te = 2.653, for a = 0.01 and df = 65.294. The rejection region for this two-tailed test is R = {t: t > 2.653}. (3) Test Statistics Since it is assumed that the population variances are unequal, the t-statistic is computed as follows: t= 41-X 0.81682 -0.82410 == -4.634 V 43607 + 0.0057012

(4) Decision about the null hypothesis Since it is observed that t = 4.634 >te = 2.653, it is then concluded that the null hypothesis is rejected. Using the P-value approach: The p-value is p=0, and since p=0 <0.01, it is concluded that the null hypothesis is rejected.

(5) Conclusion

there is enough evidence to claim that population mean weight of coke​ is different than mean weight of pepsi​, at the 0.01 significance level.