Question SAMPLING DISTRIBUTIONS AND ESTIMATION; HYPOTHESIS TESTIN

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 –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< –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?

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