BUS 240 TEST 3 | QUESTIONS AND ANSWERS

BUS 240 TEST 3 | QUESTIONS AND ANSWERS Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was 50,000 miles with a standard deviation of 3,500 miles. What is the estimated average tread life in miles for the entire population of these tires? 50,000 A population has a known standard deviation of 25. A simple random sample of 49 items is taken from the selected population. The sample mean (x-bar) IS 300. What is the margin of error at the 95% confidence level? 7 Knowing the population standard deviation, a 95% confidence interval infers that the population mean ______. A. is between 0 and 100% B. is within +- 1.96 standard deviations of the sample mean C. is within +- standard errors of the sample mean D. is too large A survey of an urban university (population of 25,450) showed that 870 of 1100 students sampled attended a home football game during the season. What inferences can be made about student attendance at football games? (0.759, 0.823) The distribution of Student's t is Symmetrical Which of the following would you use as a point estimate for the population mean? Sample mean. A university surveyed recent graduates of the English Department for their starting salaries. Four hundred graduates returned the survey. The average salary was $25,000, with a standard deviation of $2,500. What is the best point estimate of the population mean? $25,000 University officials say that at least 70% of the voting student population supports a fee increase. If the 95% confidence interval estimating the proportion of students supporting the fee increase is [0.75, 0.85], what conclusion can be drawn? The interval estimate is above 70%, so infer that it will be supported. Which statement(s) is/are correct about the t distribution? All apply. (the mean is zero, its shape is symmetric, its dispersion is based on the degrees of freedom) The z-score or z-value corresponding to a 95.34% confidence interval is ________. 1.99 A random sample of 20 items is selected from a population. When computing a confidence interval for the population mean, what number of degrees of freedom should be used to determine the appropriate t-value? 19 A random sample of 42 college graduates revealed that they worked an average of 5.5 years on the job before being promoted. The sample standard deviation was 1.1 years. Using the 0.99 degree of confidence, what is the confidence interval for the population mean? 5.04 and 5.96 A sample standard deviation is the best point estimate of the ___________. population standard deviation There are 2,000 eligible voters in a precinct. A total of 500 voters are randomly selected and asked whether they plan to vote for the Democratic incumbent or the Republican challenger. Of the 500 surveyed, 350 said they would vote for the Democratic incumbent. Using the 0.99 confidence coefficient, what are the confidence limits for the proportion that plan to vote for the Democratic incumbent? 0.647 and 0.753 A research firm wants to compute an interval estimate with 90% confidence for the mean time to complete an employment test. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour? 98 A sample of 500 students is selected from a known population of 15000 students to construct a 99% confidence interval for the average SAT score. What correction factor should be used to compute the standard error? 0.9832 Suppose 1,600 of 2,000 registered voters sampled said they planned to vote for the Republican candidate for president. Using the 0.95 degree of confidence, what is the interval estimate for the population proportion (to the nearest 10th of a percent)? 78.2% to 81.8% As the sample size for a t distribution increases, the differences between the t distribution and the standard normal distribution: become smaller, as the t distribution approaches the standard normal distribution. A random sample of 85 supervisors revealed that they worked an average of 6.5 years before being promoted. The population standard deviation was 1.7 years. Using the 0.95 degree of confidence, what is the confidence interval for the population mean? 6.14 and 6.86 When using Student's t to compute an interval estimate, ___________. we assume that the samples are collected from normally distributed populations A local retail company wants to estimate the mean amount spent by customers. Their store's budget limits the number of surveys to 225. What is their maximum error of the estimated mean amount spent for a 99% level of confidence and an estimated standard deviation of $10.00? $1.72 The mean weight of trucks traveling on a particular section of I-475 is not known. A state highway inspector needs an estimate of the population mean. He selects and weighs a random sample of 49 trucks and finds the mean weight is 15.8 tons. The population standard deviation is 3.8 tons. What is the 95% confidence interval for the population mean? 14.7 and 16.9 A research firm needs to estimate within 3% the proportion of junior executives leaving large manufacturing companies within three years. A 0.95 degree of confidence is to be used. Several years ago, a study revealed that 21% of junior executives left their company within three years. To update this study, how many junior executives should be surveyed? 709 What is the interpretation of a 96% confidence level? Approximately 96 out of 100 such intervals would include the true value of the population parameter. A local company wants to evaluate their quality of service by surveying their customers. Their budget limits the number of surveys to 100. What is their maximum error of the estimated mean quality for a 95% level of confidence and an estimated standard deviation of 5? 0.9604 A group of statistics students decided to conduct a survey at their university to estimate the average (mean) amount of time students spent studying per week. They sampled 554 students and found a mean of 22.3 hours per week. Assuming a population standard deviation of six hours, what is the 95% level of confidence? [21.80, 22.80] A survey of households in a small town showed that in 850 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the 99% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting? [0.674, 0.742] A survey of an urban university (population of 25,450) showed that 870 of 1,100 students sampled supported a fee increase to fund improvements to the student recreation center. Using the 95% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase? [0.767, 0.815] What kind of distribution is the t distribution? Continuous A survey of 50 retail stores revealed that the average price of a microwave was $375 with a sample standard deviation of $20. Assuming the population is normally distributed, what is the 99% confidence interval to estimate the true cost of the microwave? $367.42 to $382.58 A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 99% level of confidence, what is the confidence interval for the proportion of students attending a football game? [0.6464, 0.7172] Local government officials are interested in knowing if taxpayers are willing to support a school bond initiative that will require an increase in property taxes. A random sample of 750 likely voters was taken. Four hundred fifty of those sampled favored the school bond initiative. The 95% confidence interval for the true proportion of voters favoring the initiative is ________. [0.565, 0.635] A sample of 25 is selected from a known population of 100 elements. What is the finite population correction factor? 0.87 How is the t distribution similar to the standard z distribution? Both are continuous distributions. A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years, with a sample standard deviation of 1.5 years. What is the 95% confidence interval for the population mean? [17.95, 20.25] Which of the following is NOT necessary to determine how large a sample to select from a population? The size of the population A student wanted to construct a 95% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their average age was 19.1 years with a sample standard deviation of 1.5 years. What is the best point estimate for the population mean? 19.1 years A survey of 50 retail stores revealed that the average price of a microwave was $375, with a sample standard deviation of $20. If 90% and 95% confidence intervals were developed to estimate the true cost of the microwave, what similarities would they have? Both use the same point estimate of the population mean A student wanted to construct a 99% confidence interval for the mean age of students in her statistics class. She randomly selected nine students. Their mean age was 19.1 years with a sample standard deviation of 1.5 years. What is the 99% confidence interval for the population mean? [17.42, 20.78] A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spent studying per week. Assuming a population standard deviation of three hours, what is the required sample size if the error should be less than a half hour with a 99% level of confidence? 239 A sample of 100 is selected from a known population of 350 elements. The population standard deviation is 15. Using the finite correction factor, what is the standard error of the sample means? 1.2695 A survey of an urban university (population of 25,450) showed that 750 of 1,100 students sampled attended a home football game during the season. Using the 90% level of confidence, what is the confidence interval for the proportion of students attending a football game? [0.6591, 0.7045] If 95% and 98% confidence intervals were developed to estimate the true cost of an MP3 player with a known population standard deviation, what differences would they have? The z statistics would be different. A survey of households in a small town showed that in 500 of 1,200 sampled households, at least one member attended a town meeting during the year. Using the