Question 1

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?

Accepted Answer

A)  [17.42,20.78]
B)  [17.48,20.72]
C)  [14.23,23.98]
D)  [0.44,3.80] A

Question 2

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?

Accepted Answer

A)  $10.00
B)  $1.00
C)  1%
D)  $1.72 D

Question 3

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?

Accepted Answer

A)  ±8
B)  ±93
C)  ±7
D)  ±08 C

Question 4

Which of the following is a point estimate for the population mean (µ)?

Accepted Answer

A)  σ
B)  x/n
C)   
D)  s

Question 5

To determine the size of a sample,the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population.

Accepted Answer

A) True 
 B)False

Question 6

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?

Accepted Answer

A)  133
B)  452
C)  511
D)  2,100

Question 7

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?

Accepted Answer

A)  [0.417,0.427]
B)  [0.389,0.445]
C)  [0.400,0.417]
D)  [0.417,0.445]

Question 8

What kind of distribution is the t-distribution?

Accepted Answer

A)  Continuous
B)  Discrete
C)  Subjective
D)  A z-distribution

Question 9

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?

Accepted Answer

A)  196
B)  98
C)  10
D)  16

Question 10

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?

Accepted Answer

A)  196
B)  239
C)  15
D)  16

Question 11

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?

Accepted Answer

A)  5.04 and 5.96
B)  5.06 and 5.94
C)  2.67 and 8.33
D)  4.40 and 6.60

Question 12

As the sample size for a t-distribution increases,the differences between the t-distribution and the standard normal distribution ________.

Accepted Answer

A)  are unchanged and remain the same
B)  become smaller,as the t-distribution approaches the standard normal distribution
C)  become greater
D)  are evident because the tails of the t-distribution become thicker

Question 13

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?

Accepted Answer

A)  0.647 and 0.753
B)  0.612 and 0.712
C)  0.397 and 0.797
D)  0.826 and 0.926

Question 14

A sample of 500 students is selected from a known population of 15,000 students to construct a 99% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?

Accepted Answer

A)  0.9499
B)  0.9832
C)  2.5760
D)  Cannot be determined

Question 15

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?

Accepted Answer

A)  Both have the same confidence level.
B)  Both use the same t-statistic.
C)  Both use the same z-statistic.
D)  Both use the same point estimate of the population mean.

Question 16

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 deviation of six hours,what is the 99% level of confidence?

Accepted Answer

A)  [21.80,22.80]
B)  [16.3,28.3]
C)  [21.30,23.30]
D)  [20.22,22.0]

Question 17

An interval estimate is a single value used to estimate a population parameter.

Accepted Answer

A) True 
 B)False

Question 18

A sample standard deviation is the best point estimate of the ________.

Accepted Answer

A)  population range
B)  population skewness
C)  population mode
D)  population standard deviation

Question 19

When using the t-distribution to calculate a confidence interval,we assume that the population of interest is normal or nearly normal.

Accepted Answer

A) True 
 B)False

Question 20

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?

Accepted Answer

A)  Seventy percent is not in the interval,so another sample is needed.
B)  Seventy percent is not in the interval,so assume it will not be supported.
C)  The interval estimate is above 70%,so infer that it will be supported.
D)  Since this was not based on the population,no conclusion can be drawn.

Exam 9: Estimation and Confidence Intervals

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?

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?

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?

Which of the following is a point estimate for the population mean (µ) ?

To determine the size of a sample,the standard deviation of the population must be estimated by either taking a pilot survey or by approximating it based on knowledge of the population.

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?

What kind of distribution is the t-distribution?

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?

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?

As the sample size for a t-distribution increases,the differences between the t-distribution and the standard normal distribution ________.

A sample of 500 students is selected from a known population of 15,000 students to construct a 99% confidence interval for the average SAT score. What correction factor should be used to compute the standard error?

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?

An interval estimate is a single value used to estimate a population parameter.

A sample standard deviation is the best point estimate of the ________.

When using the t-distribution to calculate a confidence interval,we assume that the population of interest is normal or nearly normal.

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?