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Business Stats Ch. 9 Test Bank Exam
Papers With Correct Answers 2025/
The mean number of travel days per year for salespeople employed by three hardware distributors needs to be estimated with a 0.90 degree of confidence. For a small pilot study, the mean was 150 days and the standard deviation was 14 days. If the population mean is estimated within two days, how many salespeople should be sampled?
133
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
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.
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.
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.
A bank wishes to estimate the mean credit card balance owed by its customers. The population standard deviation is estimated to be $300. If a 98% confidence interval is used and an interval of $75 is desired, how many customers should be sampled?
87
Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The results showed that the mean tread life was 50,000 miles, with a standard deviation of 3,500 miles. What is the best estimate of the mean tread life in miles for the entire population of these tires?
50,
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.
Which of the following is NOT necessary to determine how large a sample to select from a population?
The size of the population
A sample mean is the best point estimate of _______.
the population mean
A sample standard deviation is the best point estimate of the ___________.
population standard deviation
A confidence interval for a population mean __________.
estimates a likely interval for a population mean
Knowing the population standard deviation, a 95% confidence interval infers that the population mean ___________.
is within ±1.96 standard errors of the sample mean
When a confidence interval for a population mean is constructed from sample data, __________.
we can conclude, for an infinite number of samples and corresponding confidence intervals, that the population mean is in a stated percentage of the intervals
The distribution of Student's t has _________.
a mean of zero and a standard deviation that depends on the sample size
The distribution of Student's t is ________.
symmetrical
When using Student's t to compute an interval estimate, ___________.
we assume that the samples are collected from normally distributed populations
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.
When we use a confidence interval to reach a conclusion about the population mean, we are applying a type of reasoning or logic called __________.
statistical inference
The likelihood that any confidence interval based on a sample of 400 graduates will contain the population mean is 0.95.
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]
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 99% level of confidence, what is the confidence interval for the proportion of students supporting the fee increase?
[0.759, 0.823]
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.
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 six hours, what is the required sample size if the error should be less than a half hour with a 95% level of confidence?
554
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 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 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. They sampled 240 students and found a mean of 22. hours per week. Assuming a population standard deviation of six hours, what is the 99% level of confidence?
[21.30, 23.30]
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 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]
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 survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. What is the 95% confidence interval to estimate the true cost of a gallon of milk?
$2.77 to $3.
A survey of 25 grocery stores revealed that the average price of a gallon of milk was $2.98, with a standard error of $0.10. What is the 98% confidence interval to estimate the true cost of a gallon of milk?
$2.73 to $3.
A survey of 25 grocery stores revealed that the mean price of a gallon of milk was $2.98, with a standard error of $0.10. If 90% and 95% confidence intervals were developed to estimate the true cost of a gallon of milk, what similarities would they have?
Both use the same point estimate of the population mean
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]
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]
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 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 95% level of confidence, what is the confidence interval for the proportion of households represented at a town meeting?
[0.389, 0.445]
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
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.
The z-score or z-value corresponding to a 95.34% confidence interval is ________.
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]
