Question 1

The t distribution allows the calculation of confidence intervals for means for small
samples when the population variance is not known, regardless of the shape of the distribution in the
population.

Accepted Answer

The t distribution assumes that the underlying population from which the sample is drawn is normally distributed, especially important when dealing with small sample sizes.

Question 2

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of
250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval
for the proportion of cases of recidivism would go from __________ to __________.

Accepted Answer

The answer of A prison official wants to estimate the...

Question 3

Private colleges and universities rely on money contributed by individuals and corporations for their operating expenses. Much of this money is put into a fund called an endowment, and the college
Spends only the interest earned by the fund. A recent survey of 8 private colleges in the United States
Revealed the following endowments (in millions of dollars): 60.2, 47.0, 235.1, 490.0, 122.6, 177.5,
95)4, and 220.0. Summary statistics yield $$\bar { X } = 180.975 \text { and } S = 143.042$$ . Calculate a 95%
Confidence interval for the mean endowment of all the private colleges in the United States assuming
A normal distribution for the endowments. a) $\$ 180.975 \pm \$ 94.066$
b) $\$ 180.975 \pm \$ 99.123$
c) $\$ 180.975 \pm \$ 116.621$
d) $\$ 180.975 \pm \$ 119.586$

Accepted Answer

The answer of Private colleges and universities rely on money...

Question 4

The county clerk wants to estimate the proportion of voters who will need special election facilities.
The clerk wants to construct a 95% confidence interval for the population proportion which extends
at most 0.07 to either side of the sample proportion. How large a sample must be taken to assure
these conditions are met?

Accepted Answer

The answer of The county clerk wants to estimate the...

Question 5

The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

Accepted Answer

The statement does not provide enough information to determine its truthfulness, as it simply states a value (34.32) as the upper bound of a 90% confidence interval estimate of the population mean without context or contradiction.

Question 6

The confidence interval estimate of the population proportion is constructed around the
sample proportion.

Accepted Answer

This is true. The confidence interval estimate of the population proportion is based on the sample proportion as it is used as the point estimate for the population proportion.

Question 7

A university dean is interested in determining the proportion of students who receive some sort of
financial aid. Rather than examine the records for all students, the dean randomly selects 200 students
and finds that 118 of them are receiving financial aid. Use a 90% confidence interval to estimate the
true proportion of students who receive financial aid.

Accepted Answer

The answer of A university dean is interested in determining...

Question 8

A sample of 100 fuses from a very large shipment is found to have 10 that are
defective. The 95% confidence interval would indicate that, for this shipment, the proportion of
defective fuses is between 0 and 0.28.

Accepted Answer

The lower bound of a 95% confidence interval for a proportion cannot be less than 0. The correct statement would be that the interval indicates that the proportion of defective fuses is between 0.04 and 0.16.

Question 9

Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of
10 data points, a 90% confidence interval will have a width of 2.36.

Accepted Answer

The width of a confidence interval is determined by the level of confidence, sample size, and sample standard deviation. It is not determined by the sample mean alone. Therefore, the statement is false.

Question 10

A major department store chain is interested in estimating the mean amount its credit card customers spent on their first visit to the chain's new store in the mall. Fifteen credit card accounts were
Randomly sampled and analyzed with the following results: $\bar { X } = \$ 50.50 \text { and } S = 20$ . Construct a
95% confidence interval for the mean amount its credit card customers spent on their first visit to the
Chain's new store in the mall assuming that the amount spent follows a normal distribution. a) $\$ 50.50 \pm \$ 9.09$
b) $\$ 50.50 \pm \$ 10.12$
c) $\$ 50.50 \pm \$ 11.00$
d) $\$ 50.50 \pm \$ 11.08$

Accepted Answer

The answer of A major department store chain is interested...

Question 11

In estimating the population mean with the population standard deviation unknown, if
the sample size is 12, there will be 6 degrees of freedom.

Accepted Answer

In estimating the population mean with the population standard deviation unknown, if the sample size is n, there will be n-1 degrees of freedom, so for a sample size of 12, there will be 11 degrees of freedom.

Question 12

A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a
mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0
to 60 mean time is 4.52 seconds to 5.18 seconds.

Accepted Answer

The answer of A race car driver tested his car...

Question 13

The county clerk wants to estimate the proportion of voters who will need special election facilities.
Suppose a sample of 400 voters was taken. If 150 need special election facilities, calculate an 90%
confidence interval for the population proportion.

Accepted Answer

The answer of The county clerk wants to estimate the...

Question 14

The t distribution allows the calculation of confidence intervals for means when the
actual standard deviation is not known.

Accepted Answer

This is true. The t distribution takes into account the sample size and uses the sample standard deviation to estimate the population standard deviation, allowing for the calculation of confidence intervals for the mean.

Question 15

A quality control engineer is interested in estimating the proportion of defective items coming off a
production line. In a sample of 300 items, 27 are defective. A 90% confidence interval for the
proportion of defectives from this production line would go from __________ to __________.

Accepted Answer

The answer of A quality control engineer is interested in...

Question 16

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of
250 convicts, the official determines that there are 65 cases of recidivism. A confidence interval will
be obtained for the proportion of cases of recidivism. Part of this calculation includes the estimated
standard error of the sample proportion. For this sample, the estimated standard error is __________.

Accepted Answer

The answer of A prison official wants to estimate the...

Question 17

In forming a 90% confidence interval for a population mean from a sample size of 22,
the number of degrees of freedom from the t distribution equals 22.

Accepted Answer

The number of degrees of freedom from the t distribution equals n - 1, where n is the sample size. Therefore, for a sample size of 22, the number of degrees of freedom from the t distribution would be 21.

Question 18

A university dean is interested in determining the proportion of students who receive some sort of financial aid. Rather than examine the records for all students, the dean randomly selects 200 students
And finds that 118 of them are receiving financial aid. The 95% confidence interval for π is 0.59 ±
0)07. Interpret this interval.
A) We are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.
B) 95% of the students get between 52% and 66% of their tuition paid for by financial aid.
C) We are 95% confident that between 52% and 66% of the sampled students receive some sort of financial aid.
D) We are 95% confident that 59% of the students are on some sort of financial aid.

Accepted Answer

The confidence interval of 0.59 ± 0.07 means we are 95% confident that the true proportion of all students receiving financial aid is between 0.52 and 0.66.

Question 19

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate
the mean number of people who are admitted to the emergency room during a 24-hour period. The
director randomly selects 64 different 24-hour periods and determines the number of admissions for
each. For this sample, $\bar { X } = 396 \text { and } S = 100$ . Estimate the mean number of admissions per 24-hour
period with a 95% confidence interval.

Accepted Answer

The answer of As an aid to the establishment of...

Question 20

As an aid to the establishment of personnel requirements, the director of a hospital wishes to estimate the mean number of people who are admitted to the emergency room during a 24-hour period. The
Director randomly selects 64 different 24-hour periods and determines the number of admissions for
Each. For this sample, $\bar { X } = 396 \text { and } S = 100$ . Which of the following assumptions is necessary in
Order for a confidence interval to be valid?
A) The population sampled from has an approximate normal distribution.
B) The population sampled from has an approximate t distribution.
C) The mean of the sample equals the mean of the population.
D) None of these assumptions are necessary.

Accepted Answer

The answer of As an aid to the establishment of...

Quiz 8: Confidence Interval Estimation

The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from to .

The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

The confidence interval estimate of the population proportion is constructed around the sample proportion.

A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be 6 degrees of freedom.

A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.

The county clerk wants to estimate the proportion of voters who will need special election facilities. Suppose a sample of 400 voters was taken. If 150 need special election facilities, calculate an 90% confidence interval for the population proportion.

The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 300 items, 27 are defective. A 90% confidence interval for the proportion of defectives from this production line would go from to .

In forming a 90% confidence interval for a population mean from a sample size of 22, the number of degrees of freedom from the t distribution equals 22.

Quiz 8: Confidence Interval Estimation

The t distribution allows the calculation of confidence intervals for means for small samples when the population variance is not known, regardless of the shape of the distribution in the population.

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from __________ to __________.

The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

The confidence interval estimate of the population proportion is constructed around the sample proportion.

A sample of 100 fuses from a very large shipment is found to have 10 that are defective. The 95% confidence interval would indicate that, for this shipment, the proportion of defective fuses is between 0 and 0.28.

Given a sample mean of 2.1 and a sample standard deviation of 0.7 from a sample of 10 data points, a 90% confidence interval will have a width of 2.36.

In estimating the population mean with the population standard deviation unknown, if the sample size is 12, there will be 6 degrees of freedom.

A race car driver tested his car for time from 0 to 60 mph, and for 20 tests obtained a mean of 4.85 seconds with a standard deviation of 1.47 seconds. A 95% confidence interval for the 0 to 60 mean time is 4.52 seconds to 5.18 seconds.

The county clerk wants to estimate the proportion of voters who will need special election facilities. Suppose a sample of 400 voters was taken. If 150 need special election facilities, calculate an 90% confidence interval for the population proportion.

The t distribution allows the calculation of confidence intervals for means when the actual standard deviation is not known.

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 300 items, 27 are defective. A 90% confidence interval for the proportion of defectives from this production line would go from __________ to __________.

In forming a 90% confidence interval for a population mean from a sample size of 22, the number of degrees of freedom from the t distribution equals 22.

A prison official wants to estimate the proportion of cases of recidivism. Examining the records of 250 convicts, the official determines that there are 65 cases of recidivism. A 99% confidence interval for the proportion of cases of recidivism would go from to .

A quality control engineer is interested in estimating the proportion of defective items coming off a production line. In a sample of 300 items, 27 are defective. A 90% confidence interval for the proportion of defectives from this production line would go from to .