The Gidget Company makes widgets. If the production process is working properly, it turns out that the widgets are normally distributed with a mean length of at least 2.6 feet. Larger widgets can be used or altered but shorter widgets mustE scrapped. You select a sample of 25 widgets, and the mean length is 2.46 feet and the sample standard deviation is 0.16 foot. Do you need to adjust the production equipment? Complete parts (a) through (d). Click here to view page 1 of the critical values for the t Distribution. Click here to view page 2 of the critical values for the t Distribution, Since tne test statistic is iess tnan tne criticai vaiue, reject the nuii nypotnesis ana conciuoe tnat tnere is suTIcieht eviaence tnat you neea to aajust tne proauction equipment. b. If you test the null hypothesis at the 0.05 level significance, what decision do you make using the p-value approach to hypothesis testing? What is the p-value for this test? 0.0001 (Round to four decimal places as needed.) What is the conclusion for this test? Since the p-value is the null hypothesis and conclude that there is sufficient evidence that you need to adjust the production equipment. less than a, reject c. Interpret the meaning of the p-value in this problem. Choose the correct answer below. A. The p-value is the probability that the sample of widgets have a mean length of 2.46 feet or less, given that the the mean length is actually 2.6 feet. O B. The p-value is the probability that the sample of widgets have a mean length of 2.6 feet or greater. OC. The p-value is the probability that the sample of widgets have a mean length of 2.6 feet or greater, given that the the mean length is actually 2.46 feet. O D. The p-value is the probability that the sample of widgets have a mean length of 2.46 feet or less. d. Compare your conclusions in (a) and (b). Choose the correct answer below. O A. Using the critical value approach the null hypothesis was not rejected and using the p-value approach the null hypothesis was not rejected. The critical value approach and the p-value approach are two different methods of finding the same answer. O B. Using the critical value approach, the null hypothesis was not rejected and using the p-value approach, the null hypothesis was rejected. The critical value approach and the p-value approach yeild opposite results. O C. Using the critical value approach, the null hypothesis was rejected and using the p-value approach, the null hypothesis was not rejected. The critical value approach and the p-value approach yield opposite results. O D. Using the critical value approach the null hypothesis was rejected and using the p-value approach the null hypothesis was rejected. The critical value approach and the p-value approach are two different methods of finding the same answer.