STAT 2606 E: BUSINESS STATISTICS IASSIGNMENT 4DUE IN CLASS MONDAY, MARCH 25, 2019INSTRUCTIONS:I. Assignments are to be submitted in class prior to beginning of class on the due date.II. For written questions, show all of your work. No credit will be given for answers without justification.Do not use MINITAB for a question unless it specifically says to do so.III. No late assignments will be accepted.1. A federal agency responsible for enforcing laws concerning weights and measures routinely inspectspackages to determine whether the weight of the contents is at least as great as that advertised on thepackage. A simple random sample of 25 observations of a product whose container claims that the net weightis 10 ounces yielded a mean of 9.48 ounces and a variance of 1.43 ounces2. Do these data provide sufficientevidence to enable the agency to conclude that the true mean net weight is lower than the net weightindicated on the container? Use ? = 0.05 . Give the conditions under which this test is valid.2. A research manager at Coca-Cola claims that the true proportion, p, of cola drinkers that prefer CocaColaover Pepsi is greater than 0.50. In a consumer taste test, 100 randomly selected people were given blindsamples of Coca-Cola and Pepsi. 58 of these subjects preferred Coca-Cola. Is there sufficient evidence at the5% level of significance to validate Coca-Cola’s claim? Conduct an appropriate hypothesis test using (i) thep-value method and (ii) the rejection point method.3. A fast food company uses two management-training methods. Method 1 is a traditional method of trainingand Method 2 is a supposedly new and innovative method. The company has just hired thirty-one (31) newmanagement trainees. Fifteen (15) of the trainees are randomly selected and assigned to Method 1 and theremaining 16 trainees are assigned to Method 2. After three months of training, the management traineestook a standardized test. The test was designed to evaluate their performance and learning from training. Thesample mean score and sample standard deviation of the two methods are given below. The managementwants to determine if the company should implement the new training method.Conduct an appropriate hypothesis test at the 5% level of significance to determine if there is a difference inthe average score between the two methods. Conduct this test using (i) the p-value method, (ii) the criticalvalue method, and (iii) the confidence interval method. Give the conditions under which this test is valid. Method x s1 69 3.42 72 3.84. An experimental surgical procedure is being studied as an alternative to the old method. Both methods areconsidered safe. Five surgeons perform the operation using both methods on two patients matched by age,sex, and other relevant factors, with the time to complete the surgery (in minutes) recorded below.Surgeon Old Method New Method1 36 292 55 423 28 304 40 325 62 56At the 1% level of significance, does the new method decrease the average length of the surgical procedure?Give the conditions under which this test is valid.5. The digital music players produced by a large Canadian manufacturer during the first two months of 2010were of poor quality. A random sample of 100 players was obtained during this time and the players weretested. It was determined that 25 of them were defective. As a result, quality control standards were thentightened. A random sample of 100 players was taken during the next two months, 11 of which weredefective. Is there sufficient evidence to indicate that the new quality control standards were effective inreducing the proportion of defective digital music players? To answer this question, conduct a hypothesistest at the 5% level of significance.6. MINITAB QUESTION. Hypothesis testing for when is known.Imagine choosing n = 16 women at random from a large population and measuring their heights. Assumethat the heights of the women in this population are normally distributed with = 63.8 inches and = 3inches. Suppose you then test the null hypothesis H0: = 63.8 versus the alternative that Ha : 63:8,using = 0.10. Simulate the results of doing this test 100 times by entering the following commands:MTB > random 16 c1-c100;SUBC > normal 63.8 3.MTB > ztest 63.8 3 c1-c100(A) In how many of these hypothesis tests did you reject H0? In how many of these hypothesis tests did youexpect to reject H0?(B) Are the p-values all the same for the 100 tests? Why or why not?(C) Suppose you used = 0.01 instead of = 0.10. Does this change any of your decisions to reject ornot? In how many of these hypothesis tests did you expect to reject H0? In general, should the number ofrejections increase or decrease if = 0.01 is used instead of = 0.10?(D) Now assume that the population really has a mean of = 63 instead of 63.8. Carry out the above 100simulations again by changing the command “normal 63.8 3.” to “normal 63 3.” Once again, using = 0.10. In how many tests did you reject H0? In how many of these hypothesis tests did you expect toreject H0?(E) Is a rejection of H0 in part (A) a correct decision? If not, what type of error are you making in rejectingH0?(F) Is a rejection of H0 in part (D) a correct decision? 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