A. Must Always Be Smaller Than the Population Mean Μ

Study Questions

1. Since the sample size [n] is always smaller than the size of the population [N], then the sample mean [ ] [3-116] a. must always be smaller than the population mean [µ] b. must be larger than the population mean [µ] c. must be equal to the population mean [µ] d. must be zero e. None of the above is correct

2. Whenever the population has a normal probability distribution, the sampling distribution of the sample mean [ ] has a normal probability distribution [16-118] a. for only large sample sizes b. for only small sample sizes c. for any sample size d. for only sample sizes ≥ 30 e. None of the above is correct

3. A simple random sample from an infinite population is a sample selected such that [5-116] a. each element selected comes from the same population b. each element is selected independently c. both a and b must be satisfied d. the probability of being selected changes e. None of the above is correct

4. If we consider the simple random sampling process as an experiment, the sample mean [ ] is [10-117] a. always zero b. always smaller than the population mean [µ] c. a random variable d. exactly equal to the population mean [µ] e. None of the above is correct

5. The confidence associated with an interval estimate is called [2-143] a. significance b. degree of association c. confidence level d. precision e. None of the above is correct 6. From a population which is normally distributed, a sample of [n=25 elements] is selected and the standard deviation [s] of the sample is computed. For the interval estimation of the population mean [µ], the proper distribution to use is the [10-145] a. normal distribution b. t distribution c. t distribution with 25 degrees of freedom d. t distribution with 24 degrees of freedom e. None of the above answers is correct

7. A 95% confidence interval for a population mean [µ] shows the values 25.1 to 28.3. What is the appropriate conclusion? [16-147] a. 95% of all sample means [ ] should be between 25.1 to 28.3 b. 95% of the time, the population mean [µ] will be within this interval; 5% of the time it will be outside this interval c. Since 95% of all confidence intervals contain the population mean [µ], we are 95% confident this interval includes it d. All of the above answers are correct e. Nonce of the above answers are correct

8. In determining the sample size [n] necessary to estimate a population proportion [P], which of the following information is NOT needed? [22-148] a. the maximum size of the sampling error that can be tolerated b. the confidence level required c. a preliminary estimate of the true population proportion [P] d. the mean of the population [µ] e. None of the above is correct

9. In hypothesis testing, if valid sample data indicate the null hypothesis is to be rejected, [2-167] a. no conclusions can be drawn from the test b. the alternative hypothesis may also be rejected c. the data must have been accumulated incorrectly d. the sample size [n] was too small e. None of the above answers is correct

10. The level of significance in hypothesis testing is the probability of [7-168] a. not rejecting a true null hypothesis b. not rejecting a false null hypothesis c. rejecting a true null hypothesis d. could be any of the above, depending upon the situation e. None of the above is correct 11. If a hypothesis test leads to the rejection of the null hypothesis [17-171] a. a Type I error is always committed b. a Type II error is always committed c. a Type I error may have been committed d. a Type II error may have been committed e. None of the above is correct

12. For a two-tailed test and a sample size of [n=40], the null hypothesis will NOT be rejected at the 5% level if the standardized test statistic is [38-177] a. between -1.96 and 1.96 b. greater than 1.96 c. less than 1.645 d. greater than -1.645 e. None of the above answers is correct

13. The mean wage rate for hourly workers at General Motors is [µ =$14.25] per hour (Detroit News, April 14, 1989). Assume that the population standard deviation [=$2.00]. What is the probability that the sample mean [ ] is at least $13.80 per hour, given a random sample of [n=50 workers]? [38-233] a. .0559 b. .4441 c. .5559 d. .9441 e. None of the above is correct

14. The average weekly earnings of the plumbers in a city is [µ=$750] with a standard deviation of [ =$40]. Assume that we select a random sample of [n=64 plumbers], what is the probability that the sample mean [ ] will be greater than $740? [15-281] a. .0228 b. .0987 c. .4772 d. .5987 e. None of the above is correct 15. The owner of a major Atlanta restaurant wanted to estimate the mean amount spent per customer for dinner meals. A random sample of [n=49 customers] over a 3-week period revealed a sample average of [ =$12.60] spent, with a population standard deviation [ =$2.50]. Determine a 95% confidence interval (rounded to the nearest cent) for the average amount spent per dinner meal of all his customers. [5-260] a. $12.01 to $13.19 b. $11.76 to $13.44 c. $11.90 to $13.30 d. Unable to determine because of insufficient data e. None of the above is correct

16. A random sample of [n=64 children] of working mothers showed that they were absent from school a sample average of [ =5.3] days per term, with a standard deviation [s=1.8 days]. Provide a 96% confidence interval for the average number of days absent per term for all the students. a. 5.2321 days to 5.3762 days b. 4.8151 days to 5.7543 days c. 4.8387 days to 5.7612 days d. 4.7722 days to 5.8392 days e. None of the above is correct

17. Tuff-Wear Tire Company, in Findlay, Ohio, wants its advertising company to put together an ad campaign that will claim its low-end cost line tires will last at least [µ=28,000 miles]. Tests with a random sample [n=30 tires] show a sample mean [ =27,500 miles] with a sample standard deviation [s=1000 miles]. At a .05 level of significance, these tests indicate [18-300] a. Reject H0: Z of -2.7386 < -1.6450 b. Reject H0: Z of -2.7386 < 1.6450 c. Do not reject H0: Z of 1.6450 < 2.7386 d. Do not reject H0: Z of -1.6450 < 2.7386 e. None of the above is correct

18. From a population of cereal boxes marked “12 ounces”, a random sample of [n=16 boxes] is selected and the contents of each box is weighed. The sample revealed a sample mean [ =11.7 ounces], with a standard deviation [s=0.8 ounces]. Test to see if the population mean [µ] is at least 12 ounces. Use a 0.05 level of significance. [4-332] a. Reject H0: t of 1.753 > -1.500 b. Reject H0: t of -1.500 < -1.753 c. Do not reject H0: t of -1.645 > -1.753 d. Do not reject H0: t of -1.500 < 1.753 e. None of the above is correct 19. In the town of Springdale, 30% of the families [P =.30] regularly plant vegetable gardens. A random sample of [n=100 families] is selected for a particular study. What is the probability that the sample proportion [ ], the proportion of families who plant a vegetable garden, is between (.20) and (.40)? a. .0146 b. .0292 c. .4854 d. .9708 e. None of the above is correct

20. The proprietor of a boutique in New York wanted to determine the average age of his customers. A random sample of [n=25 customers] revealed an average age of [ =32 years], with a standard deviation of [s=8 years]. Determine a 95% confidence interval estimate for the average age of all his customers. a. 28.6976 to 35.3024 b. 28.8640 to 35.1360 c. 29.2624 to 34.7376 d. 29.3680 to 34.6320 e. None of the above is correct

21. The U.S. Bureau of Census reported mean hourly earnings in the wholesale trade industry of [µ =$9.70 per hour] in 1987. A random sample of [n=49] wholesale trade workers in a particular city showed a sample mean hourly wage of [ =$9.30 per hour] with a standard deviation of [s=$1.05 per hour]. Use H0:µ = $9.70 and Ha: µ ≠ $9.70. Test to see if wage rates in the city differ significantly from the reported $9.70. Use α = .05 [25-703] a. Reject H0: Z of 2.6667 > 1.960 b. Reject H0: Z of 2.6667 > 1.645 < c. Reject H0: Z of -2.6667 < -1.960 d. Do not reject H0: Z of 0.3810 < 1.960 e. None of the above is correct