You construct a 95% confidence interval for a population mean using a random sample. The confidence interval is 24.9 < µ < 31.5. Is the probability that µ is in this interval 0.95? Explain.
> Use the data set to a. find the sample mean, b. find the sample standard deviation, and c. construct a 99% confidence interval for the population mean. Assume the population is normally distributed. The grade point averages of 14 randomly selected co
> Use the data set to a. find the sample mean, b. find the sample standard deviation, and c. construct a 99% confidence interval for the population mean. Assume the population is normally distributed. The SAT scores of 12 randomly selected high school
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. About 60% of U.S
> You research repair costs of mobile devices and find that the population mean is $89.56. In Exercise 20, does the t-value fall between -t0.95 and t0.95?
> You research prices of cell phones and find that the population mean is $431.61. In Exercise 19, does the t-value fall between -t0.95 and t0.95?
> You research driving distances to work and find that the population standard deviation is 5.2 miles. Repeat Exercise 18 using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results.
> You research commute times to work and find that the population standard deviation is 9.3 minutes. Repeat Exercise 17 using the standard normal distribution with the appropriate calculations for a standard deviation that is known. Compare the results. F
> You are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
> Find the critical value tc for the level of confidence c and sample size n. c = 0.95, n = 12
> You are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
> You are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
> You are given the sample mean and the sample standard deviation. Assume the population is normally distributed and use the t-distribution to find the margin of error and construct a 95% confidence interval for the population mean. Interpret the results.
> Use the confidence interval to find the margin of error and the sample mean. (16.2, 29.8)
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. One out of every
> Use the confidence interval to find the margin of error and the sample mean. (64.6, 83.6)
> Use the confidence interval to find the margin of error and the sample mean. (6.17, 8.53)
> Use the confidence interval to find the margin of error and the sample mean. (14.7, 22.1)
> Construct the indicated confidence interval for the population mean µ using the t-distribution. Assume the population is normally distributed. c = 0.99, x = 24.7, σ = 4.6, n = 50
> Construct the indicated confidence interval for the population mean µ using the t-distribution. Assume the population is normally distributed. c = 0.98, x = 4.3, σ = 0.34, n = 14
> Construct the indicated confidence interval for the population mean µ using the t-distribution. Assume the population is normally distributed. c = 0.95, x = 13.4, σ = 0.85, n = 8
> Find the critical value tc for the level of confidence c and sample size n. c = 0.90, n = 10
> Use the values on the number line to find the sampling error. X = 3.8 µ = 4.27 +++X 3.4 3.6 3.8 4.0 4.2 4.4 4.6
> Find the critical value zc necessary to construct a confidence interval at the level of confidence c. c = 0.97
> Find the critical value zc necessary to construct a confidence interval at the level of confidence c. c = 0.75
> Seventy-seven percent of U.S. college students pay their bills on time. You randomly select five U.S. college students and ask them whether they pay their bills on time. The random variable represents the number of U.S. college students who pay their bil
> Find the critical value zc necessary to construct a confidence interval at the level of confidence c. c = 0.85
> The equation for determining the sample size can be obtained by solving the equation for the margin of error for n. Show that this is true and justify each step. 2. n E E Vn
> Use the finite population correction factor to construct each confidence interval for the population mean. a. c = 0.99, x = 8.6, σ = 4.9, N = 200, n = 25 b. c = 0.90, x = 10.9, σ = 2.8, N = 500, n = 50 c. c = 0.95, x = 40.3, σ = 0.5, N = 300, n = 68
> Determine the finite population correction factor for each value of N and n. a. N = 1000 and n = 500 b. N = 1000 and n = 100 c. N = 1000 and n = 75 d. N = 1000 and n = 50 e. N = 100 and n = 50 f. N = 400 and n = 50 g. N = 700 and n = 50 h. N = 120
> When all other quantities remain the same, how does the indicated change affect the minimum sample size requirement? Explain. a. Increase in the level of confidence b. Increase in the error tolerance c. Increase in the population standard deviation
> When estimating the population mean, why not construct a 99% confidence interval every time?
> A tennis ball manufacturer wants to estimate the mean circumference of tennis balls within 0.05 inch. Assume the population of circumferences is normally distributed. a. Determine the minimum sample size required to construct a 99% confidence interval f
> A soccer ball manufacturer wants to estimate the mean circumference of soccer balls within 0.15 inch. a. Determine the minimum sample size required to construct a 99% confidence interval for the population mean. Assume the population standard deviation
> A beverage company uses a machine to fill half-gallon bottles with fruit juice (see figure). The company wants to estimate the mean volume of water the machine is putting in the bottles within 0.25 fluid ounce. a. Determine the minimum sample size requi
> A paint manufacturer uses a machine to fill gallon cans with paint (see figure). The manufacturer wants to estimate the mean volume of paint the machine is putting in the cans within 0.5 ounce. Assume the population of volumes is normally distributed. a
> The table shows the ages of students in a freshman orientation course. a. Construct a probability distribution. b. Graph the probability distribution using a histogram and describe its shape. c. Find the mean, variance, and standard deviation of the p
> An admissions director wants to estimate the mean age of all students enrolled at a college. The estimate must be within 1.5 years of the population mean. Assume the population of ages is normally distributed. a. Determine the minimum sample size requir
> Find the critical value zc necessary to construct a confidence interval at the level of confidence c. c = 0.80
> A cheese processing company wants to estimate the mean cholesterol content of all one-ounce servings of a type of cheese. The estimate must be within 0.75 milligram of the population mean. a. Determine the minimum sample size required to construct a 95%
> Determine the minimum sample size required when you want to be 99% confident that the sample mean is within two units of the population mean and σ = 1.4. Assume the population is normally distributed.
> Determine the minimum sample size required when you want to be 95% confident that the sample mean is within one unit of the population mean and σ = 4.8. Assume the population is normally distributed.
> Use the information to construct 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. The sodium chloride concentrations (in grams per liter) for 36 randomly selected seawater
> Use the information to construct 90% and 99% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. A group of researchers estimates the mean length of time (in minutes) the average U.S. ad
> Describe how you would construct a 90% confidence interval to estimate the population mean age for students at your school.
> When all other quantities remain the same, how does the indicated change affect the width of a confidence interval? Explain. a. Increase in the level of confidence b. Increase in the sample size c. Increase in the population standard deviation
> In Exercise 38, does it seem possible that the population mean could be less than 100? Explain.
> Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. (a) 5 10 15 20 P(x) 0.03 0.09 0.19 0.32 0.37 (b) 1 4 5 6 P(x) 20 10 3. 10 25 3. 2.
> In Exercise 37, does it seem possible that the population mean could be greater than 90°F? Explain.
> In Exercise 36, does it seem possible that the population mean could be within 1% of the sample mean? Explain.
> In Exercise 35, does it seem possible that the population mean could equal the sample mean? Explain.
> You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sampl
> You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sampl
> You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sampl
> You are given the sample mean and the population standard deviation. Use this information to construct 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals. From a random sampl
> Use the confidence interval to find the estimated margin of error. Then find the sample mean. A store manager reports a confidence interval of (244.07, 280.97) when estimating the mean price (in dollars) for the population of textbooks.
> Use the confidence interval to find the estimated margin of error. Then find the sample mean. A government agency reports a confidence interval of (26.2, 30.1) when estimating the mean commute time (in minutes) for the population of workers in a city.
> Find the indicated probabilities using the geometric distribution, the Poisson distribution, or the binomial distribution. Then determine whether the events are unusual. If convenient, use a table or technology to find the probabilities. The mean increas
> Determine the minimum sample size n needed to estimate m for the values of c, σ, and E. c = 0.98, σ = 10.1, E = 2
> Determine the minimum sample size n needed to estimate m for the values of c, σ, and E. c = 0.80, σ = 4.1, E = 2
> Determine the minimum sample size n needed to estimate m for the values of c, σ, and E. c = 0.95, σ = 2.5, E = 1
> For the same sample statistics, which level of confidence would produce the widest confidence interval? Explain your reasoning. a. 90% b. 95% c. 98% d. 99%
> Determine the minimum sample size n needed to estimate m for the values of c, σ, and E. c = 0.90, σ = 6.8, E = 1
> Use the confidence interval to find the margin of error and the sample mean. (3.144, 3.176)
> Use the confidence interval to find the margin of error and the sample mean. (1.71, 2.05)
> Use the confidence interval to find the margin of error and the sample mean. (21.61, 30.15)
> Use the confidence interval to find the margin of error and the sample mean. (12.0, 14.8)
> Construct the indicated confidence interval for the population mean µ. c = 0.80, x = 20.6, σ = 4.7, n = 100
> a. find the mean, variance, and standard deviation of the probability distribution, and b. interpret the results. The number of cell phones per household in a small town Cell phones 1 2 3 4 5 6 Probability 0.020 0.140 0.272 0
> Construct the indicated confidence interval for the population mean µ. c = 0.99, x = 10.50, σ = 2.14, n = 45
> Construct the indicated confidence interval for the population mean µ. c = 0.95, x = 31.39, σ = 0.80, n = 82
> Construct the indicated confidence interval for the population mean µ. c = 0.90, x = 12.3, σ = 1.5, n = 50
> Match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics. c = 0.98 (a) 54.9 57.2 59.5 (b) 55.2 57.2 59.2 54 55 56 57 58 59 60 54 55 56 57 58 59 60 (c) 55.6
> Which statistic is the best unbiased estimator for µ? a. σ b. x c. the median d. the mode
> Match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics. c = 0.95 (a) 54.9 57.2 59.5 (b) 55.2 57.2 59.2 54 55 56 57 58 59 60 54 55 56 57 58 59 60 (c) 55.6
> Match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics. c = 0.90 (a) 54.9 57.2 59.5 (b) 55.2 57.2 59.2 54 55 56 57 58 59 60 54 55 56 57 58 59 60 (c) 55.6
> Match the level of confidence c with the appropriate confidence interval. Assume each confidence interval is constructed for the same sample statistics. c = 0.88 (a) 54.9 57.2 59.5 (b) 55.2 57.2 59.2 54 55 56 57 58 59 60 54 55 56 57 58 59 60 (c) 55.6
> Find the margin of error for the values of c, σ, and n. c = 0.975, σ = 4.6, n = 100
> Find the margin of error for the values of c, σ, and n. c = 0.80, σ = 1.3, n = 75
> Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. The random variable x represents the number of classes in which a student is enrolled in a given semester at a university. 1 3 5 P
> Find the margin of error for the values of c, σ, and n. c = 0.90, σ = 2.9, n = 50
> Find the margin of error for the values of c, σ, and n. c = 0.95, σ = 5.2, n = 30
> Use the values on the number line to find the sampling error. I = 46.56 u = 48.12 46 47 48 49
> Use the values on the number line to find the sampling error. u = 24.67 I= 26.43 24 25 26 27
> Use the values on the number line to find the sampling error. µ = 8.76 I = 9.5 +++++X 8.6 8.8 9.0 9.2 9.4 9.6 9.8
> When estimating a population mean, are you more likely to be correct when you use a point estimate or an interval estimate? Explain your reasoning.
> Write the binomial probability in words. Then, use a continuity correction to convert the binomial probability to a normal distribution probability. P(x < 25)
> Match the binomial probability statement with its corresponding normal distribution probability statement (a)–(d) after a continuity correction. P(x < 109) a. P(x > 109.5) b. P(x < 108.5) c. P(x < 109.5) d. P(x > 108.5)
> Match the binomial probability statement with its corresponding normal distribution probability statement (a)–(d) after a continuity correction. P(x ≤ 109) a. P(x > 109.5) b. P(x < 108.5) c. P(x < 109.5) d. P(x > 108.5)
> Match the binomial probability statement with its corresponding normal distribution probability statement (a)–(d) after a continuity correction. P(x ≥ 109) a. P(x > 109.5) b. P(x < 108.5) c. P(x < 109.5) d. P(x > 108.5)
> Determine whether the distribution is a probability distribution. If it is not a probability distribution, explain why. The random variable x represents the number of tickets a police officer writes out each shift. 1 2 3 4 5 P(x) 0.09 0.23 0.29 0.16
> Match the binomial probability statement with its corresponding normal distribution probability statement (a)–(d) after a continuity correction. P(x > 109) a. P(x > 109.5) b. P(x < 108.5) c. P(x < 109.5) d. P(x > 108.5)
> The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Determine whether you can use a normal distribution to approximate the distribution of x. n = 20, p = 0.65, q = 0.35
> A drug manufacturer claims that a drug cures a rare skin disease 75% of the time. The claim is checked by testing the drug on 100 patients. If at least 70 patients are cured, then this claim will be accepted. Find the probability that the claim will be a
> A drug manufacturer claims that a drug cures a rare skin disease 75% of the time. The claim is checked by testing the drug on 100 patients. If at least 70 patients are cured, then this claim will be accepted. Find the probability that the claim will be r
> The figure shows the results of a survey of U.S. adults ages 33 to 51 who were asked whether they participated in a sport. Seventy percent of U.S. adults ages 33 to 51 said they regularly participated in at least one sport, and they gave their favorite s
> The sample size n, probability of success p, and probability of failure q are given for a binomial experiment. Determine whether you can use a normal distribution to approximate the distribution of x. n = 18, p = 0.90, q = 0.10
> The figure shows the results of a survey of U.S. adults ages 33 to 51 who were asked whether they participated in a sport. Seventy percent of U.S. adults ages 33 to 51 said they regularly participated in at least one sport, and they gave their favorite s
> A survey of U.S. adults found that 8% believe the biggest problem in schools today is poor teaching. You randomly select a sample of U.S. adults. Find the probability that more than 100 U.S. adults believe the biggest problem in schools today is poor tea
> About 3.3% of hourly paid U.S. workers earn the prevailing minimum wage or less. A grocery chain offers discount rates to companies that have at least 30 employees who earn the prevailing minimum wage or less. Find the probability that each company will
> Determine whether you can use a normal distribution to approximate the binomial distribution. If you can, use the normal distribution to approximate the indicated probabilities and sketch their graphs. If you cannot, explain why and use a binomial distri
