A manufacturer of hand-held calculators receives large shipments of printed circuits from a supplier. It is too costly and time-consuming to inspect all incoming circuits, so when each shipment arrives, a sample is selected for inspection. Information from the sample is then used to test Ho: P = 0.01 versus H₂: p > 0.01, where p is the actual proportion of defective circuits in the shipment. If the null hypothesis is not rejected, the shipment is accepted, and the circuits are used in the production of calculators. If the null hypothesis is rejected, the entire shipment is returned to the supplier because of inferior quality. (A shipment is defined to be of inferior quality if it contains more than 1% defective circuits.) (a) In this context, define Type I and Type II errors. (Select all that apply.) A Type I error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective. A Type I error is not obtaining convincing evidence that more than 1% of a shipment is defective when in fact more than 1% of the shipment is defective. □ A Type II error is not obtaining convincing evidence that more than 1% of a shipment is defective when in fact more than 1% of the shipment is defective. A Type II error is obtaining convincing evidence that more than 1% of a shipment is defective when in fact (at most) 1% of the shipment is defective. (b) From the calculator manufacturer's point of view, which type of error is considered more serious? O A Type I error, as the calculator manufacturer would use defective circuits in the calculators. O A Type II error, as the calculator manufacturer would use defective circuits in the calculators. (c) From the printed circuit supplier's point of view, which type of error is considered more serious? O A Type I error as the supplier would receive back, and not be paid for, a shipment of circuits that was in fact acceptable. O A Type II error as the supplier would receive back, and not be paid for, a shipment of circuits that was in fact acceptable.

A U.S. Food Survey showed that Americans routinely eat beef in their diet. Suppose that in a study of 49 consumers in Illinois and 64 consumers in Texas the following results were obtained from two samples regarding average yearly beef consumption:               Illinois                                     Texas              = 49                                     = 64                                                 = 54.1lb                              = 60.4lb             S1 = 7.0                                    S2 = 8.0   Formulate a hypothesis so that, if the null hypothesis is rejected, we can conclude that the average amount of beef eaten annually by consumers in Illinois is significantly less than that eaten by consumers in Texas.

A researcher wonders if a “majority” of all residents of a particular city were in favor of a newly proposed city ordinance. Her hypotheses are H0: p = 0.5 versus Ha: p > 0.5. She collected data from a large enough random sample of residents (in order to use the normal approximation), and the resulting sample proportion was 0.41. The researcher has a few interns working on this project and has asked them to conduct the appropriate test and report an approximate p-value. Unfortunately, she received three different p-values from her interns:  Chris reported a p-value of 0.08 Jamie reported a p-value of 0.41 Taylor reported a p-value of 0.62   A. Which of her interns reported a reasonable p-value? Explain. Hint: The precise p-value cannot be computed here, but you can eliminate interns' guesses. B. Use the p-value from part (a) to determine if a majority of all residents of the city were in favor of a newly proposed city ordinance.

A snack food manufacturer estimates that the variance of the number of grams of carbohydrates in servings of its tortilla chips is 1.17. A dietician is asked to test this claim and finds that a random sample of 19 servings has a variance of 1.29. At α=0.05​, is there enough evidence to reject the​ manufacturer's claim? Assume the population is normally distributed. Complete parts​ (a) through​ (e) below.       ​(a) Write the claim mathematically and identify H0 and Ha.     A. H0​: σ2≤1.17 ​(Claim) Ha​: σ2>1.17   B. H0​: σ2≠1.17 Ha​: σ2=1.17 ​(Claim)   C. H0​: σ2=1.17 ​(Claim) Ha​: σ2≠1.17 Your answer is correct.   D. H0​: σ2≥1.17 Ha​: σ2<1.17 ​(Claim) ​(b) Find the critical​ value(s) and identify the rejection​ region(s).   The critical​ value(s) is(are) enter your response here. ​(Round to two decimal places as needed. Use a comma to separate answers as​ needed.)

A company is doing a hypothesis test on the variation of quality from two suppliers. They believe that one of the suppliers has a different variance than the other supplier and would like to perform a hypothesis test to support their claim. Both distributions are normal, and the populations are independent. use a = 0.01 Ho: σ12- σ2 2 HA:0 1 Supplier 1: standard deviation = 3.54, Sample size = 24 Supplier 2: standard deviation = 8, Sample size = 29. The test statistic (rounded to 4 decimal places) is = The p-value (rounded to 4 decimal places) is = O Reject the null hypothesis - there is enough evidence is support a meaningful difference in the variance of the suppliers. O Fail to reject the null hypothesis - there is not enough evidence to support a meaningful difference in the variance of the suppliers.

Solve practice question #12 and solve only parts A, B and C.

A researcher wants to know if male and female college students differ with regard to their GPAs. She randomly gets 16 male and 16 female college students to report their GPAs. The males reported a mean GPA of 3.05 with a SS = 3.75. The females reported a mean GPA of 3.1 with a SS = 2.4. You are going to be conducting an independent samples t-test. You will be conducting a two-tailed test with alpha α=.05. What is the critical t-value(s) for this test?

The human resources director of a large company recently asked her staff to conduct a study of the airline miles traveled by executives of the company during the most recent calendar year. The analyst assigned to the project randomly sampled 25 male executives and 25 female executives. Of particular interest to the HR director is whether males have greater variability in miles flown than females. The statistics available below were computed from the samples. Based on these​ data, what should the HR director conclude if an alpha level equal to 0.01 is​ used? LOADING... Click the icon to view the statistics about the number of miles flown. Males Females Mean Miles 73,262   66,888   St. Deviation Miles 2,568   1,539   Sample Size 25   25   Let sample 1 be males and sample 2 be females. What are the null and alternative​ hypotheses?     A. H0: σ21=σ22 HA: σ21≠σ22   B. H0: σ21≤σ22 HA: σ21>σ22   C. H0: σ21≥σ22 HA:…

Experiment 3: Fifteen female CSCC students and 10 male CSCC students are randomly selected to determine if the mean time studying for females is significantly more than the mean study time for males. It can be assumed that all study times are normally distributed.  Are these samples independent or dependent? Find the null and alternative hypothesis.    H0:    Ha:

Q2C. Considering the following MA(3) process: Yt=ut 0.7ut-1 - 0.2ut-2 +0.4ut-3 Where ut is a white noise process with variance equal to 1. What is the value Yk = cov(yt, Yt-k) for k = 0? Provide the correct answer along with the working steps and underlying assumptions used to calculate the value of yk = cov(yt, Yt-k) for k = 0. i. Yo = 1.69 ii. Yo = 0.63 iii. Yo = 1 iv. Yo = 0