ps5 - Econ 41 Statistics for Economists Summer 2007...

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1 Econ 41 Statistics for Economists Summer 2007 Chunming Yuan Problem Set 5 MULTIPLE CHOICE 1. A sample of 100 elements produced a mean of 48 and a standard deviation of 8. The 99% confidence interval for the population mean is: a. 44.62 to 51.38 b. 46.33 to 49.67 c. 45.94 to 50.06 d. 43.78 to 52.22 2. A sample of 27 elements produced a mean of 124 and a standard deviation of 16. Assuming that the population has a normal distribution, the 98% confidence interval for the population mean is: a. 115.50 to 132.50 b. 117.50 to 130.50 c. 114.25 to 133.75 d. 116.37 to 131.63 3. A sample of 1000 adults showed that 31% of them are smokers. The 90% confidence interval for the proportion of all adults who are smokers is: a. .300 to .320 b. .285 to .335 c. .265 to .355 d. .247 to .373 4. A company wants to estimate the mean net weight of all 32-ounce packages of its Yummy Taste cookies at a 95% confidence level. The standard deviation of net weights of all 32- ounce packages of Yummy Taste cookies is .10 ounces. The sample size that will yield a maximum error of estimate within .02 ounces of the population mean is: a. 48 b. 97 c. 191 d. 110 5. An advisor to the mayor of a large city wants to estimate, within 3 minutes, the mean travel time to work for all employees who work within the city limits. He knows that the standard deviation for all travel times is 12.25 minutes. He also wants to achieve a 95% confidence interval. He will poll a random sample of city employees. How many employees should he poll? a. 25 b. 35 c. 65

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2 d. 85 6. A researcher wants to make a 99% confidence interval for the population mean. She wants the maximum error of estimate to be within 4.8 of the population mean. The population standard deviation is 18.65. The sample size that will yield a maximum error of estimate within 4.8 of the population mean is: a. 183 b. 101 c. 54 d. 155 7. A random sample of 16 life insurance policy holders showed that the mean value of their life insurance policies is \$200,000 with a standard deviation of \$50,000. Assume that the values of life insurance policies for all such policy holders have an approximate normal distribution. The 99% confidence interval for the mean value of all life insurance policies is: a. \$174,823.50 to \$225,176.50 b. \$163,162.50 to \$236,837.50 c. \$145,249.25 to \$254,750.75 d. \$157,482.50 to \$242,517.50 8. The mean federal income tax paid last year by a sample of 36 persons selected from a city was \$4264 with a standard deviation of \$780. The 95% confidence interval for the mean federal income tax paid last year by all persons living in this city is: a. \$4009.20 to \$4518.80 b. \$4156.74 to \$4371.26 c. \$3890.41 to \$4637.59 d. \$3924.82 to \$4603.18 9. In a test of hypothesis, the Type II error occurs when: a. a false null hypothesis is rejected b. a true null hypothesis is not rejected c. a false null hypothesis is not rejected d. a true null hypothesis is rejected Use the following information to answer questions 10 – 11: In a test of hypothesis, the null hypothesis is that the population mean is equal to 80 and the
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This note was uploaded on 10/02/2008 for the course ECON ECON 41 taught by Professor Yuan during the Summer '07 term at UCLA.

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ps5 - Econ 41 Statistics for Economists Summer 2007...

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