Question 1

True or False: 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 degrees of freedom for a t-distribution in this case is the sample size minus one, which is 22 - 1 = 21.

Question 2

True or False: 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 calculated using the formula: CI width = 2 * (t-value * (s/√n)), where s is the sample standard deviation, n is the sample size, and the t-value is based on the confidence level and degrees of freedom. The given width of 2.36 does not match the calculation for a 90% confidence interval with the provided data.

Question 3

Accepted Answer

The answer of ...

Question 4

True or False: 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 sample data is drawn from a normally distributed population, especially important for small sample sizes.

Question 5

True or False: 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 True or False: A race car driver...

Question 6

True or False: The t distribution is used to develop a confidence interval estimate of the
population proportion when the population standard deviation is unknown.

Accepted Answer

The t distribution is used for estimating the population mean, not the population proportion, when the population standard deviation is unknown. For population proportions, the normal distribution is typically used.

Question 7

Accepted Answer

The answer of ...

Question 8

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 9

True or False: The confidence interval estimate of the population proportion is constructed
around the sample proportion.

Accepted Answer

The confidence interval for a population proportion is calculated using the sample proportion as the point estimate, and it provides a range of values within which the true population proportion is likely to fall.

Question 10

True or False: A random sample of 50 provides a sample mean of 31 with a standard
deviation of S = 14.The upper bound of a 90% confidence interval estimate of the population
mean is 34.32.

Accepted Answer

The upper bound of a 90% confidence interval estimate of the population mean is given by the sample mean plus the product of the critical value and the standard error of the mean. The critical value for a 90% confidence interval is 1.645, and the standard error of the mean is S/sqrt(n) = 14/sqrt(50) = 2. Therefore, the upper bound of the confidence interval is 31 + 1.645 * 2 = 34.32.

Question 11

When determining the sample size for a proportion for a given level of confidence and
Sampling error, the closer to 0.50 that π is estimated to be, the sample size required
__________.

Accepted Answer

The sample size required is larger when the estimated proportion (π) is closer to 0.50 because the variability is maximized at this point, requiring a larger sample to achieve the same level of precision.

Question 12

A confidence interval was used to estimate the proportion of statistics students who are
Females.A random sample of 72 statistics students generated the following 90% confidence
Interval: (0.438, 0.642).Based on the interval above, is the population proportion of females
Equal to 0.60?

Accepted Answer

The value 0.60 falls within the confidence interval (0.438, 0.642), so it is a plausible value for the population proportion based on the given data.

Question 13

True or False: The standardized normal distribution is used to develop a confidence interval
estimate of the population proportion regardless of whether the population standard deviation
is known.

Accepted Answer

The standardized normal distribution (Z-distribution) is used for confidence intervals of population proportions because the standard deviation of the sample proportion can be estimated using the sample data, regardless of the population standard deviation.

Question 14

True or False: 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 answer of True or False: A sample of 100...

Question 15

Accepted Answer

The answer of ...

Question 16

True or False: 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

The degrees of freedom for estimating the population mean with an unknown population standard deviation is calculated as the sample size minus one, so it would be 11 for a sample size of 12.

Question 17

Accepted Answer

The answer of ...

Question 18

True or False: The standardized normal distribution is used to develop a confidence interval
estimate of the population proportion when the sample size is sufficiently large.

Accepted Answer

The standardized normal distribution (Z-distribution) is used for confidence intervals of population proportions when the sample size is large enough to satisfy the conditions for normal approximation.

Question 19

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

Accepted Answer

The t distribution is used to estimate population parameters when the sample size is small and the population standard deviation is unknown.

Question 20

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...

Quiz 8: Confidence Interval Estimation

True or False: 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.

True or False: 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.

True or False: 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.

True or False: 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.

True or False: The t distribution is used to develop a confidence interval estimate of the population proportion when the population standard deviation is unknown.

True or False: The confidence interval estimate of the population proportion is constructed around the sample proportion.

True or False: A random sample of 50 provides a sample mean of 31 with a standard deviation of S = 14.The upper bound of a 90% confidence interval estimate of the population mean is 34.32.

When determining the sample size for a proportion for a given level of confidence and Sampling error, the closer to 0.50 that π is estimated to be, the sample size required __________.

A confidence interval was used to estimate the proportion of statistics students who are Females.A random sample of 72 statistics students generated the following 90% confidence Interval: (0.438, 0.642) .Based on the interval above, is the population proportion of females Equal to 0.60?

True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion regardless of whether the population standard deviation is known.

True or False: 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.

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

True or False: The standardized normal distribution is used to develop a confidence interval estimate of the population proportion when the sample size is sufficiently large.

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