Math 2311 EMCF Homework 10 Sections 7.4 - 7.5 Honework will NOT be accepted through email or in person. Homework must be submitted through CourseWare, https://www.casa.uh.edu, before the deadline. Submit this assignment on CourseWare under \"EMCF\" and choose ehw10. 1. As the sample size increases, the margin of error increases decreases stays the same increases or decreases depending on the size of the mean all of these above sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m a. b. c. d. e. 2. The t* value for a 95% confidence interval estimation with 24 degrees of freedom is a. b. c. d. e. 1.711 2.064 2.492 2.069 1.96 3. In interval estimation, the t distribution is applicable only when a. b. c. d. e. the population has a mean of less than 30 the sample standard deviation (s) is given instead of the population standard deviation () the variance of the population is known the standard deviation of the population is known we will always use the t distribution 4. To assess the precision of a laboratory scale, we measure a block known to have a mass of 1 gram. We measure the block n times and record the mean x of the measurements. Suppose the scale readings are normally distributed with unknown mean and standard deviation = 0.001 g. How large should n be so that a 95% confidence interval for has a margin of error of 0.0001? 20 385 10,000 66,358 384 Th a. b. c. d. e. 5. When estimating a population mean by a sample mean, which of the following does the margin of error not depend on? a. b. c. d. e. The The The The The sample size sample mean confidence level population standard deviation margin of error depends on all of these. https://www.coursehero.com/file/16942999/ehw10pdf/ 1 6. A Census Bureau report on the income of Americans says that with 95% confidence the mean income of all U.S. households in 2006 was $57,010 with a margin of error of $350. This means that a. 95% of all households had incomes in the range $57,010 $350. b. We can be sure that the mean income for all households in the country lies in the range $57,010 $350. c. We are 95% confident that the mean household income of all Americans will be in the range $57,010 $350 d. 95% of the households in the sample interviewed by the Census Bureau had incomes in the range $57,010 $350. e. We are 95% confident that the mean household income is $57,010. 7. You have measured the systolic blood pressure of a random sample of 25 employees of a company located near you. A 95% confidence interval for the mean systolic blood pressure for the employees of this company is (122, 138). Which of the following statements gives a valid interpretation of the confidence level? sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m a. 95% of the sample of employees have a systolic blood pressure between 122 and 138. b. 95% of the population of employees have a systolic blood pressure between 122 and 138. c. If the procedure were repeated many times, 95% of the resulting confidence intervals would contain the population mean systolic blood pressure. d. The probability that the population mean blood pressure is between 122 and 138 is .95 8. If the 98% confidence limits for the population mean are 73 and 80, which of the following could be the 95% confidence limits? a. b. c. d. e. 73 and 81 72 and 79 72 and 81 74 and 79 none of these 9. A 95% confidence interval for the mean reading achievement score for a population of third grade students is (44.2, 54.2). Suppose you compute a 99% confidence interval using the same information. Which of the following statements is correct? a. b. c. d. The intervals have the same width. The 99% interval is longer. The 99% interval is shorter. None of the above. 10. Which of the following confidence intervals will be the smallest? 80% 95% 90% 98% Th a. b. c. d. https://www.coursehero.com/file/16942999/ehw10pdf/ 2 sh is ar stu ed d vi y re aC s o ou urc rs e eH w er as o. co m 11. A test engineer wants to estimate the mean gas mileage ~ (in miles per gallon) for a particular model of automobile. Eleven of these cars are subjected to a road test, and the gas mileage is computed for each car. A dotplot of the 11 gas-mileage values is roughly symmetrical and has no outliers. The mean and standard deviation of these values are 25.5 and 3.01, respectively. Assuming that these 11 automobiles can be considered a simple random sample of cars of this model, which of the following is a correct statement? \u0013 \u0012 3.01 . a. A 95% confidence interval for is 25.5 2.228 \u0012 11 \u0013 3.01 b. A 95% confidence interval for is 25.5 2.201 . \u0012 11 \u0013 3.01 c. A 95% confidence interval for is 25.5 2.228 . \u0012 10 \u0013 3.01 . d. A 95% confidence interval for is 25.5 2.201 10 e. The results cannot be trusted; the sample is too small. 12. Which of the following statements is (are) true about the t-distribution with k-degrees of freedom? I. The t-distribution is symmetric. II. The t-distribution with k degrees of freedom has a smaller variance than the t-distribution with k + 1 degrees of freedom. III. The t-distribution has a larger variance than the standard normal (z) distribution. a. b. c. d. e. f. I only II only III only I and III I and II none of these 13. What is the critical value t* which satisfies the condition that the t distribution with 8 degrees of freedom for an 80% confidence interval? a. b. c. d. e. 1.397 1.282 2.89 0.90 none of these 14. A 95% confidence interval for the mean reading achievement score for a population of third-grade students is (44.2, 54.2). The margin of error of this interval is 5 5% 2.5 54.2 cannot be determined Th a. b. c. d. e. 15. Refer to the previous problem. The sample mean is a. b. c. d. e. 0.95 54.2 44.2 49.2 cannot be determined https://www.coursehero.com/file/16942999/ehw10pdf/ Powered by TCPDF (www.tcpdf.org) 3