Question

0142 Day 21. Secs. 6.1 and 6.2 Hypothesis Testing page 2 of 1 2. An ad campaign for Nabisco said that there were at least 1000 chips in every bag of Chips Ahoy cookies. A group of Air Force Cadets did an experiment to test the claim. They got bags from stores across the country. They dissolved the cookies in each bag in cold water so that they could easily count the chips by hand. They collected a sample of 42 bags and found an average of 1261.6 chips per bag, with standard deviation of 117.6 chips. Test whether the average number of chips per bag was at least 1000

Answer 1

The provided sample mean is X = 1261.6 and the sample standard deviation is s = 117.6, and the sample size is n = 42. (1) Null and Alternative Hypotheses The following null and alternative hypotheses need to be tested: Ho: u = 1000 Ha: u > 1000 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 a = 0.05, and the critical value for a right-tailed test is te = 1.683. The rejection region for this right-tailed test is R=t:t>1.683 (3) Test Statistics The t-statistic is computed as follows: t = X Mo s/n 1261.6 - 1000 117.6/42 = 14.416 (4) Decision about the null hypothesis Since it is observed that t = 14.416 > te = 1.683, 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 < 0.05, 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 u is greater than 1000, at the 0.05 significance level. Confidence Interval The 95% confidence interval is 1224.953<u < 1298.247.

Therefore, we conclude that the average number of chips per bag is atleast 1000

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