Question 1

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:
A) 2.7969
B) 2.7874
C) 2.4922
D) 2.4851

Accepted Answer

To find the critical value of t, we use the t-distribution table with degrees of freedom (df) = n-1 = 24 and a confidence level of 99%. Looking at the table, the closest value to 2.7969 is the value at the intersection of df = 24 and 99% confidence level, which is 2.4922. However, since the table only provides values for certain degrees of freedom and certain values of confidence levels, we need to choose the closest value possible. In this case, the closest value is 2.7969, which corresponds to a confidence level slightly higher than 99%. Therefore, the answer is choice A.

Question 2

A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 48.5 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 time is 45.2 seconds to 51.8 seconds.

Accepted Answer

The given information does not provide any clear indication of whether the stated confidence interval is true or false. The confidence interval may or may not be accurate based on the sample size, distribution, and assumptions.

Question 3

If a sample has 18 observations and a 90% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.740.

Accepted Answer

This statement is true as the appropriate value of t for a 90% confidence interval with 18 degrees of freedom is indeed 1.740.

Question 4

A robust estimator is one that is:
A) unbiased and symmetrical about zero.
B) consistent and is also mound-shaped.
C) efficient and less spread out.
D) not sensitive to moderate nonnormality.

Accepted Answer

A robust estimator is one that is not sensitive to moderate nonnormality. This means that the estimator gives accurate results even if the distribution of the data is not perfectly normal. Therefore, option D is the best choice.

Question 5

In forming a 95% confidence interval for a population mean from a sample size of 20, the number of degrees of freedom from the t-distribution equals 20.

Accepted Answer

The number of degrees of freedom from the t-distribution equals 19 for a sample size of 20.

Question 6

Researchers determine that 60 Puffs tissues is the average number of tissues used during a cold.Suppose a random sample of 100 Puffs users yielded the following data on the number of tissues used during a cold: = 52 and s = 22.Using the sample information provided, the value of the test statistic is: A) t = (52 - 60) / 22 B) t = (52- 60) / (22 / 100) C) t = (52- 60) / (22 / 100²) D) t = (52 - 60) / (22 / 10)

Accepted Answer

The answer of Researchers determine that 60 Puffs tissues is...

Question 7

The statistic  when the sampled population is normal is Student t-distributed with n degrees of freedom.

Accepted Answer

The answer of The statistic  when the sampled population...

Question 8

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42.If the 10% level of significance were used in testing the hypotheses H₀: $\mu$ = 201 vs.H₁: $\mu$$\neq$201, the null hypothesis: A) would be rejected. B) would be accepted. C) would fail to be rejected. D) would become H₀: $\mu$ $\neq$ 201

Accepted Answer

Since the null hypothesis states that the population mean is equal to 201, which falls outside of the 90% confidence interval limits of 170.86 and 195.42, there is sufficient evidence to reject the null hypothesis at the 10% level of significance.

Question 9

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n -1 because we lose one degree of freedom by using the:
A) sample mean as an estimate of the population mean.
B) sample standard deviation as an estimate of the population standard deviation.
C) sample proportion as an estimate of the population proportion.
D) sample size as an estimate of the population size.

Accepted Answer

The answer of For statistical inference about the mean of...

Question 10

In order to determine the p-value associated with hypothesis testing about the population mean $\mu$, it is necessary to know the value of the test statistic.

Accepted Answer

The answer of In order to determine the p-value associated...

Question 11

If a sample has 15 observations and a 95% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.753.

Accepted Answer

The answer of If a sample has 15 observations and...

Question 12

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25.The upper limit of a 95% confidence interval for the population mean would equal:
A) 77.77
B) 72.23
C) 88.85
D) 77.27

Accepted Answer

The answer of A random sample of size 15 taken...

Question 13

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

Accepted Answer

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown. The formula for the confidence interval is dependent on the sample size and the degrees of freedom, which are determined by the sample size and whether an estimate of the population standard deviation is used.

Question 14

In estimating the population mean with the population standard deviation unknown, if the sample size is 16, there are 8 degrees of freedom.

Accepted Answer

The degrees of freedom for estimating the population mean with unknown population standard deviation and sample size n is (n-1). Therefore, in this case with a sample size of 16, the degrees of freedom would be 15.

Question 15

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 16

A major electronics store chain is interested in estimating the average 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: = $50.50 and s² = 400.A 95% confidence interval for the average amount the credit card customers spent on their first visit to the chain's new store in the mall is: A) $50.50 $9.09. B) $50.50 $10.12. C) $50.50 $11.08. D) None of these choices.

Accepted Answer

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

Question 17

The t-distribution is used in a confidence interval for a mean when the actual standard error is not known.

Accepted Answer

The t-distribution is used when the sample size is small and the population standard deviation is not known, and is used in calculating confidence intervals for population means.

Question 18

The t-distribution assumes that the population is normally distributed.

Accepted Answer

The answer of The t-distribution assumes that the population is...

Question 19

In order to interpret the p-value associated with hypothesis testing about the population mean $\mu$, it is necessary to know the value of the test statistic.

Accepted Answer

The p-value is the probability of obtaining a test statistic as extreme as or more extreme than the one observed, assuming the null hypothesis is true. Therefore, the p-value can be interpreted without knowing the exact value of the test statistic.

Question 20

If the sampled population is nonnormal, the t-test of the population mean $\mu$ is still valid, provided that the condition is not extreme.

Accepted Answer

The t-test of the population mean is robust to moderate deviations from normality, as long as the sample size is large enough. However, if the nonnormality is extreme or the sample size is very small, then the t-test may not be valid and alternative methods may be necessary.

Quiz 12: Inference About a Population

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:

A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 48.5 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 time is 45.2 seconds to 51.8 seconds.

If a sample has 18 observations and a 90% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.740.

A robust estimator is one that is:

In forming a 95% confidence interval for a population mean from a sample size of 20, the number of degrees of freedom from the t-distribution equals 20.

The statistic when the sampled population is normal is Student t-distributed with n degrees of freedom.

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42.If the 10% level of significance were used in testing the hypotheses H₀: $\mu$ = 201 vs.H₁: $\mu$ $\neq$ 201, the null hypothesis:

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n -1 because we lose one degree of freedom by using the:

In order to determine the p-value associated with hypothesis testing about the population mean $\mu$ , it is necessary to know the value of the test statistic.

If a sample has 15 observations and a 95% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.753.

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25.The upper limit of a 95% confidence interval for the population mean would equal:

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

In estimating the population mean with the population standard deviation unknown, if the sample size is 16, there are 8 degrees of freedom.

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.

The t-distribution is used in a confidence interval for a mean when the actual standard error is not known.

The t-distribution assumes that the population is normally distributed.

In order to interpret the p-value associated with hypothesis testing about the population mean $\mu$ , it is necessary to know the value of the test statistic.

If the sampled population is nonnormal, the t-test of the population mean $\mu$ is still valid, provided that the condition is not extreme.

Quiz 12: Inference About a Population

For a 99% confidence interval of the population mean based on a sample of n = 25 with s = 0.05, the critical value of t is:

A race car driver tested his car for time from 0 to 60 mph, and in 20 tests obtained an average of 48.5 seconds with a standard deviation of 1.47 seconds.A 95% confidence interval for the 0 to 60 time is 45.2 seconds to 51.8 seconds.

If a sample has 18 observations and a 90% confidence estimate for μ\muμ is needed, the appropriate value of t is 1.740.

A robust estimator is one that is:

In forming a 95% confidence interval for a population mean from a sample size of 20, the number of degrees of freedom from the t-distribution equals 20.

The statistic when the sampled population is normal is Student t-distributed with n degrees of freedom.

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42.If the 10% level of significance were used in testing the hypotheses H0: μ\muμ = 201 vs.H1: μ\muμ≠\neq= 201, the null hypothesis:

For statistical inference about the mean of a single population when the population standard deviation is unknown, the degrees for freedom for the t-distribution equal n -1 because we lose one degree of freedom by using the:

In order to determine the p-value associated with hypothesis testing about the population mean μ\muμ , it is necessary to know the value of the test statistic.

If a sample has 15 observations and a 95% confidence estimate for μ\muμ is needed, the appropriate value of t is 1.753.

A random sample of size 15 taken from a normally distributed population revealed a sample mean of 75 and a sample variance of 25.The upper limit of a 95% confidence interval for the population mean would equal:

The t-distribution is used to develop a confidence interval estimate of the population mean when the population standard deviation is unknown.

In estimating the population mean with the population standard deviation unknown, if the sample size is 16, there are 8 degrees of freedom.

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.

The t-distribution is used in a confidence interval for a mean when the actual standard error is not known.

The t-distribution assumes that the population is normally distributed.

In order to interpret the p-value associated with hypothesis testing about the population mean μ\muμ , it is necessary to know the value of the test statistic.

If the sampled population is nonnormal, the t-test of the population mean μ\muμ is still valid, provided that the condition is not extreme.

If a sample has 18 observations and a 90% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.740.

Based on sample data, the 90% confidence interval limits for the population mean are LCL = 170.86 and UCL = 195.42.If the 10% level of significance were used in testing the hypotheses H₀: $\mu$ = 201 vs.H₁: $\mu$ $\neq$ 201, the null hypothesis:

In order to determine the p-value associated with hypothesis testing about the population mean $\mu$ , it is necessary to know the value of the test statistic.

If a sample has 15 observations and a 95% confidence estimate for $\mu$ is needed, the appropriate value of t is 1.753.

In order to interpret the p-value associated with hypothesis testing about the population mean $\mu$ , it is necessary to know the value of the test statistic.

If the sampled population is nonnormal, the t-test of the population mean $\mu$ is still valid, provided that the condition is not extreme.