SAMPLING DISTRIBUTIONS AND ESTIMATION; HYPOTHESIS TESTING

Questions 1 to 20:Select the best answer to each question. Note that a question and its answers may be split across a page

break, so be sure that you have seen theentirequestion andallthe answers before choosing an answer.

1.Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis

that the population mean isnotequal to 52. Assume we have collected 38 sample data from which we

computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample

data appear approximately normal. What is thep-value you would report for this test?

A.0.0041

B.0.4963

C.0.0074

D.0.0037

2.For 1996, the U.S. Department of Agriculture estimated that American consumers would have eaten, on

average, 2.6 pounds of cottage cheese throughout the course of that year. Based on a longitudinal study of

98 randomly selected people conducted during 1996, the National Center for Cottage Cheese Studies found

an average cottage cheese consumption of 2.75 pounds and a standard deviation ofs= 14 ounces. Given

this information, which of the following statements would becorrectconcerning a two-tail test at the 0.05

level of significance?

A.We can conclude that the average cottage cheese consumption in America isn’t 2.6 pounds per person per year.

B.We can conclude that the average cottage cheese consumption in America is at least 0.705 pound more or less than 2.75

pounds per person per year.

C.We can conclude that we can’t reject the claim that the average cottage cheese consumption in America is 2.6 pounds per

person per year.

D.We can conclude that the average cottage cheese consumption in America is actually 2.75 pounds per person per year.

3.In sampling without replacement from a population of 900, it’s found that the standard error of the

mean, , is only two-thirds as large as it would have been if the population were infinite in size. What is

the approximate sample size?

A.600

B.200

C.500

D.400

4.A portfolio manager was analyzing the price-earnings ratio for this year’s performance. His boss said that

the average price-earnings ratio was 20 for the many stocks that his firm had traded, but the portfolio

manager felt that the figure was too high. He randomly selected a sample of 50 price-earnings ratios and

found a mean of 18.17 and a standard deviation of 4.60. Assume that the population is normally

distributed, and test at the 0.01 level of significance. Which of the following is thecorrectdecision rule for

the manager to use in this situation?

A.Because 2.81 is greater than 2.33, rejectH0. At the 0.01 level, the sample data suggest that the average price-earnings ratio

for the stocks is less than 20.

B.Ifz> 2.33, rejectH0.

C.Because Â–2.81 falls in the rejection region, rejectH0. At the 0.01 level, the sample data suggest that the average priceearnings

ratio for the stocks is less than 20.

D.Ift> 2.68 or ift< Â–2.68, rejectH0. 5.In a simple random sample from a population of several hundred that's approximately normally distributed, the following data values were collected. 68, 79, 70, 98, 74, 79, 50, 102, 92, 96 Based on this information, the confidence level would be 90% that the population mean is somewhere between A.65.33 and 95.33. B.69.15 and 92.45. C.73.36 and 88.24. D.71.36 and 90.24. 6.Consider a null hypothesis stating that the population mean is equal to 52, with the research hypothesis that the population mean isnotequal to 52. Assume we have collected 38 sample data from which we computed a sample mean of 53.67 and a sample standard deviation of 3.84. Further assume the sample data appear approximately normal. What is the test statistic? A.2.68 B.2.64 C.Â–2.68 D.Â–2.64 7.Which of the following statementscorrectlycompares thet-statistic to thez-score when creating a confidence interval? A.Usingtis easier because you do not have to worry about the degrees of freedom, as you do withz. B.The value ofzrelates to a normal distribution, while the value oftrelates to a Poisson distribution. C.You can usetall the time, but forn? 30 there is no need, because the results are almost identical if you usetorz. D.Usetwhen the sample size is small, and the resulting confidence interval will be narrower. 8.Because of the popularity of movies as an entertainment medium for adolescents, an entrepreneur plans to do a national study of the average cost of a movie ticket. If you assume thats= $0.50, what sample size would the entrepreneur have to take to be 95% confident that the estimate was within $0.25 of the true mean ticket prices? A.16 B.4 C.15 D.8 9.A researcher wants to carry out a hypothesis test involving the mean for a sample ofn= 20. While the true value of the population standard deviation is unknown, the researcher is reasonably sure that the population is normally distributed. Given this information, which of the following statements would be correct? A.The researcher should use thez-test because the sample size is less than 30. B.Thet-test should be used because the sample size is small. C.The researcher should use thez-test because the population is assumed to be normally distributed. D.Thet-test should be used because?and?are unknown. 10.What is the purpose of sampling? A.To verify that the population is approximately normally distributed B.To create a point estimator of the population mean or proportion C.To estimate a target parameter of the population D.To achieve a more accurate result than can be achieved by surveying the entire population 11.H0isp= 0.45 andH1isp? 0.45. What type of test will be performed? A.Two-tail testing of a mean B.One-tail testing of a mean C.Two-tail testing of a proportion D.One-tail testing of a proportion 12.What is theprimaryreason for applying a finite population correction coefficient? A.If you don't apply the correction coefficient, your confidence intervals will be too broad, and thus less useful in decision making. B.When the sample is a very small portion of the population, the correction coefficient is required. C.If you don't apply the correction coefficient, you won't have values to plug in for all the variables in the confidence interval formula. D.If you don't apply the correction coefficient, your confidence intervals will be too narrow, and thus overconfident. 13.Which of the following statements aboutp-value testing istrue? A.Theprepresents sample proportion. B.P-value testing uses a predetermined level of significance. C.P-value testing applies only to one-tail tests. D.Thep-value is the lowest significance level at which you should rejectH0. 14.What sample size is required from a very large population to estimate a population proportion within 0.05 with 95% confidence? Don't assume any particular value forp. A.271 B.38 C.767 D.385 15.If a teacher wants to test her belief that more than five students in college classes typically receive A as End of exam a grade, she'll perform _______-tail testing of a _______. A.two, mean B.two, proportion C.one, proportion D.one, mean 16.Determine the power for the following test of hypothesis. H0:?= 950 vs.H1:?? 950, given that?= 1,000,?= 0.10,?= 200, andn= 25. A.0.4938 B.0.3465 C.0.6535 D.0.5062 17.A random sample of 10 employees is selected from a large firm. For the 10 employees, the number of days each was absent during the past month was found to be 0, 2, 4, 2, 5, 1, 7, 3, 2, and 4. Of the following values, which would you use as the point estimate for the average number of days absent for all the firm's employees? A.3 B.4 C.2.5 D.30 18.Nondirectional assertions leadonlyto _______-tail tests. A.two B.left C.one D.right 19.Determine which of the following four population size and sample size combinations wouldnotrequire the use of the finite population correction factor in calculating the standard error. A.N= 150;n= 25 B.N= 1500;n= 300 C.N= 2500;n= 75 D.N= 15,000;n= 1,000 20.In a criminal trial, a Type II error is made when a/an A.guilty defendant is convicted. B.innocent person is convicted. C.guilty defendant is acquitted. D.innocent person is acquitted.