Probability and Statistics - Mrs. Leahy Name Chapter 6 Test Practice Questions Provide an appropriate response. 1) For a sample of 20 IQ scores the mean score is 105.8. The standard deviation,, is 15. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. Assume that IQ scores are normally distributed. A) Use normal distribution. B) Cannot use normal distribution or t-distribution. C) Use the t-distribution. 2) A random sample of 40 college students has a sample mean earnings of $3120 with a sample standard deviation of $677 over the summer months. Determine whether a normal distribution or a t-distribution should be used or whether neither of these can be used to construct a confidence interval. A) Cannot use normal distribution or t-distribution. B) Use normal distribution. C) Use the t-distribution. 3) Find the critical value zc that corresponds to a 90% confidence level. A) 1.96 B) 1.645 C) 2.58 D) 2.33 4) Find the critical value zc that corresponds to a 95% confidence level. A) 2.33 B) 2.58 C) 1.96 D) 1.645 5) Find the critical value zc that corresponds to a 99% confidence level. A) 1.96 B) 2.58 C) 1.645 D) 2.33 6) Find the critical value, tc for c = 0.99 and n = 10. A) 1.833 B) 2.262 C) 3.250 D) 3.169 1
7) Find the critical value, tc, for c = 0.95 and n = 16. A) 2.120 B) 2.602 C) 2.131 D) 2.947 8) Find the critical value, tc, for c = 0.90 and n = 15. A) 2.145 B) 1.761 C) 2.624 D) 1.753 9) Find the margin of error for the given values of c,, and n. c = 0.98, = 0.78, n = 150 A) 0.15 B) 0.08 C) 0.12 D) 0.11 10) Find the margin of error for the given values of c,, and n. c = 0.90, = 11.5, n = 120 A) 0.16 B) 0.94 C) 1.05 D) 1.73 11) Find the value of E, the margin of error, for c = 0.99, n = 16 and s = 2.6. A) 0.42 B) 0.48 C) 1.92 D) 1.69 12) Find the value of E, the margin of error, for c = 0.90, n = 10 and s = 3.1. A) 1.78 B) 1.80 C) 1.36 D) 0.57 13) A random sample of 150 students has a grade point average with a mean of x = 2.86. Assume the population standard deviation is = 0.78. Construct the confidence interval for the population mean, µ, if c = 0.98. A) (2.71, 3.01) B) (2.31, 3.88) C) (2.51, 3.53) D) (2.43, 3.79) 2
14) A random sample of 40 students has a test score with x = 81.5. Assume the population standard deviation is = 10.2. Construct the confidence interval for the population mean, µ if c = 0.90. A) (78.8, 84.2) B) (71.8, 93.5) C) (51.8, 92.3) D) (66.3, 89.1) 15) A random sample of 40 students has a mean annual earnings of x = $3120. Assume the population standard deviation is = $677. Construct the confidence interval for the population mean, µ if c = 0.95. A) ($2910, $3330) B) ($1987, $2346) C) ($4812, $5342) D) ($210, $110) 16) A random sample of 56 fluorescent light bulbs has a mean life of x =645 hours. Assume the population standard deviation is =31 hours. Construct a 95% confidence interval for the population mean. A) (712.0, 768.0) B) (112.0, 118.9) C) (636.9, 653.1) D) (539.6, 551.2) 17) Construct the indicated confidence interval for the population mean µ using the t-distribution. c = 0.95, x = 645, s = 31, n = 16 A) (628.5, 661.5) B) (321.7, 365.8) C) (531.2, 612.9) D) (876.2, 981.5) 18) Construct the indicated confidence interval for the population mean µ using the t-distribution. c = 0.99, x = 22.4, s = 3.8, n = 19 A) (16.3, 26.9) B) (17.2, 23.6) C) (19.9, 24.9) D) (18.7, 24.1) 19) Construct a 95% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 20 college students had mean annual earnings of x =$3120 with a standard deviation of s = $677. A) ($2657, $2891) B) ($1324, $1567) C) ($2135, $2567) D) ($2803, $3437) 3
20) Construct a 90% confidence interval for the population mean, µ. Assume the population has a normal distribution. A sample of 15 randomly selected students has a grade point average of x =2.86 with a standard deviation of s=0.78. A) (2.37, 3.56) B) (2.41, 3.42) C) (2.51, 3.21) D) (2.28, 3.66) 21) When 410 college students were surveyed,150 said they own their car. Find a point estimate for p, the population proportion of students who own their cars. A) 0.268 B) 0.577 C) 0.366 D) 0.634 22) A survey of 100 fatal accidents showed that 16 were alcohol related. Find a point estimate for p, the population proportion of accidents that were alcohol related. A) 0.190 B) 0.16 C) 0.138 D) 0.84 23) A survey of 700 non-fatal accidents showed that 231 involved the use of a cell phone. Find a point estimate for p, the population proportion of non-fatal accidents that involved the use of a cell phone. A) 0.670 B) 0.493 C) 0.330 D) 0.248 24) In a survey of 2480 golfers, 15% said they were left-handed. The survey's margin of error was 3%. Construct a confidence interval for the proportion of left-handed golfers. A) (0.12, 0.18) B) (0.11, 0.19) C) (0.12, 0.15) D) (0.18, 0.21) 25) A survey of 280 homeless persons showed that 63 were veterans. Construct a 90% confidence interval for the proportion of homeless persons who are veterans. A) (0.184, 0.266) B) (0.161, 0.289) C) (0.167, 0.283) D) (0.176, 0.274) 4
26) A survey of 2450 golfers showed that 281 of them are left-handed. Construct a 98% confidence interval for the proportion of golfers that are left-handed. A) (0.203, 0.293) B) (0.683, 0.712) C) (0.100, 0.130) D) (0.369, 0.451) 27) The standard IQ test has a mean of 96 and a standard deviation of 14. We want to be 99% certain that we are within 4 IQ points of the true mean. Determine the required sample size. A) 10 B) 178 C) 82 D) 1 28) In order to efficiently bid on a contract, a contractor wants to be 95% confident that his error is less than two hours in estimating the average time it takes to install tile flooring. Previous contracts indicate that the standard deviation is 4.5 hours. How large a sample must be selected? A) 19 B) 5 C) 20 D) 4 29) A researcher at a major hospital wishes to estimate the proportion of the adult population of the United States that has high blood pressure. How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 5%? A) 542 B) 9 C) 164 D) 271 30) A manufacturer of golf equipment wishes to estimate the number of left-handed golfers. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? A previous study indicates that the proportion of left-handed golfers is 9%. A) 197 B) 139 C) 19 D) 217 31) A pollster wishes to estimate the proportion of United States voters who favor capital punishment. How large a sample is needed in order to be 98% confident that the sample proportion will not differ from the true proportion by more than 3%? A) 20 B) 1068 C) 1509 D) 3017 5
32) A researcher wishes to estimate the number of households with two cars. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 5%? A previous study indicates that the proportion of households with two cars is 22%. A) 339 B) 186 C) 4 D) 264 33) A private opinion poll is conducted for a politician to determine what proportion of the population favors decriminalizing marijuana possession. How large a sample is needed in order to be 95% confident that the sample proportion will not differ from the true proportion by more than 4%? A) 13 B) 601 C) 1201 D) 423 34) A state highway patrol official wishes to estimate the number of drivers that exceed the speed limit traveling a certain road. a) How large a sample is needed in order to be 90% confident that the sample proportion will not differ from the true proportion by more than 3%? b) Repeat part (a) assuming previous studies found that 80% of drivers on this road exceeded the speed limit. 35) A certain confidence in interval is 7.75 < µ < 9.45. Find the sample mean x and the error of estimate E. 36) Use the confidence interval to find the margin of error and the sample mean. (12, 20) A) E = 8, x = 12 B) E = 4, x = 20 C) E = 8, x = 16 D) E = 4, x = 16 37) Given the same sample statistics, which level of confidence will produce the narrowest confidence interval: 75%, 85%, 90%, or 95%? Explain your reasoning. 38) The grade point averages for 10 randomly selected students in a statistics class with 125 students are listed below. 2.0 3.2 1.8 2.9 0.9 4.0 3.3 2.9 3.6 0.8 What is the effect on the width of the confidence interval if the sample size is increased to 20? Explain your reasoning. 6