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 populatio
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 the
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 incu
0.647 and 0.753
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
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 populatio
14.7 and 16.9
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
Which of the following is a point estimate for the population mean (�)?
x
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
50,000
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 statement(s) is/are correct about the t distribution?
All apply.
What kind of distribution is the t distribution?
Continuous
How is the t distribution similar to the standard z distribution?
Both are continuous distributions.
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
Of the following characteristics, the t distribution and z distribution are the same in all BUT one. Which one is it?
Mean = 0, and standard deviation = 1
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%
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 populatio
5.04 and 5.96
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
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 de
0.9604
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 d
$1.72
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 populatio
$25,000
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. The population standard deviation was $2,500. What is the 95% confidence interval for
[$24,755, $25,245]
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. The population standard deviation is $2,500. A 95% confidence interval is constructed
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 pro
[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 pro
[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
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 err
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 standar
[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 22.3 hours per week. Assuming a population standard de
[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 h
98
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 95% confidence interval to estimate the true cost of the microwave?
$369.31 to $380.69
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 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
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 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 estim
19.1 years
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 int
[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 inte
[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 $3.19
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 $3.23
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
[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
[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 represe
[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 represe
[0.389, 0.445]
A sample of 25 is selected from a known population of 100 elements. What is the finite population correction factor?
0.87
A sample of 50 is selected from a known population of 250 elements. The population standard deviation is 15. Using the finite correction factor, what is the standard error of the sample means?
1.90
A sample of 100 students is selected from a known population of 1000 students to construct a 95% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?
0.949
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 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
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 ________.
1.99
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
[0.565, 0.635]