A professor wants to know the average lifetime of batteries (in hours). To test the hypotheses, he sets 0 : 950 H μ = hours vs. 1 : 950 H μ ≠ hours, and a random sample of 25 batteries is drawn from a normal population with standard deviation 200 hours.
(1) Calculate β , the probability of a Type II error when μ = 1000 and α = 0.10 .
(2) Calculate the power of the test if n is increased from 25 to 40.
A union composed of several thousand workers prepares to vote on a new contract. To do this, a random sample of 500 workers was taken and it yielded that 340 of the workers are planning to vote YES. It is believed that the new contract will receive more than 60% YES votes
(1) Can we infer that the new contract will receive more than 60% YES votes at the 5% significance level?
(2) Compute the associated p-value for the test in (1).
Derek makes five calls per day. A sample of 200 days gives the frequencies of sales volumes listed below:
It is assumed the population follows a binomial distribution with a probability of purchasep equal to 0.50.
(1) Compute the expected frequencies for x = 0, 1, 2, 3, 4, and 5 by using the binomial probability function, Note that the rule of five should be satisfied.
(2) Should the assumption of a binomial distribution be rejected if the significance level is set at 5%?
A professor wants to investigate some of the factors that influence students’ final grade in the course. To conduct the analysis, the professor proposes the multiple regression model= β0+β1x1+β2x2+β3x3+ε, where y is the final grade (out of 100 points), 1 x is the number of lectures skipped, 2 x is the number of late assignments, and 3 x is the midterm exam score (out of 100). The professor records the data for 50 randomly selected students. The computer output is shown below.
(1) What is the adjusted coefficient of determination?
(2) Does this data provide enough evidence to conclude at the 5% significance level that the model is useful in predicting the final grade?
Ten business people who fly from Los Angeles to New York were asked to rank four airlines based on the service quality of each airline. The people assigned scores using a 5-point scale where: 1= bad, 2 = poor, 3 = average, 4 = good, and 5 = excellent. The results are shown below:
(1) Which test is appropriate if you want to compare the quality of service of the four airlines?
(2) Can we conclude that there are differences in service quality among the four airlines at the 5% significance level?
A company that manufactures shoes has three factories. Factory 1 produces 50% of the shoes, Factory 2 produces 20% shoes, and Factory 3 produces 30%. One percent of the shoes produced by Factory 1 are mislabeled, 2% of those produced by Factory 2 are mislabeled, and 0.5% of those produced by Factory 3 are mislabeled.
(1) If your friend purchases one pair of shoes from this company, what is the probability that the shoes are mislabeled?
(2) Suppose you bought a pair of shoes from this company and the shoes were correctly labeled. The next day you read in the news that the second factory employs child labor. What is the likelihood that the pair of correctly labeled shoes you bought was not manufactured there?
(3) Are the events “shoes made by Factor 2” and “shoes mislabeled” statistically independent? Explain.
A consumer research company is hired to see if three additives used in automobile gasoline improve mileage. Fourteen cars of the same make, year, and model are randomly assigned to three groups: additive A, B, and C. The data of miles per gallon (MPG)after five tanks of gasoline are recorded. Assume the data meet all ANOVA assumptions. The computer output is shown below.
(1) Does this data provide enough evidence to conclude at the 5% significance level that there is a difference in average miles per gallon (MPG) between the three additives?
(2) Report and compute an appropriate measure of effect size. Put into words what this effect size measure tells you.
(3) At the 5% significance level, use the Scheffe test to determine where the differences in average MPG truly occur. Please specify all the test statistics, the critical value, and your conclusion.
可觀看題目詳解,並提供模擬測驗!(免費會員無法觀看研究所試題解答)