Question 1

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 2

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 $\pm$ $9.09. B) $50.50 $\pm$ $10.12. C) $50.50 $\pm$ $11.08. D) None of these choices.

Accepted Answer

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

Question 3

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

Accepted Answer

The answer of When a population is small, we must...

Question 4

The t-test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

Accepted Answer

The answer of The t-test for a population mean is...

Question 5

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n - 1 degrees of freedom.

Accepted Answer

The answer of When the population standard deviation is ____________________...

Question 6

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

The null hypothesis is that the population mean is equal to 201. However, based on the given confidence interval limits, 201 is not within the range of values that we can be 90% confident the population mean falls between. Therefore, we would reject the null hypothesis at the 10% level of significance.

Question 7

Which of the following is not an example illustrating the use of variance?
A) As a measure of risk.
B) As a judge of consistency.
C) To search for and reduce variability in a process.
D) All of these choices are true.

Accepted Answer

All of these choices are true. Variance can be used as a measure of risk, as a judge of consistency, and to search for and reduce variability in a process.

Question 8

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about $\mu$is the t-distribution with n - 1 degrees of freedom.

Accepted Answer

The answer of When the population standard deviation is unknown...

Question 9

The degrees of freedom for the test statistic for $\mu$when $\sigma$ is unknown is:
A) 1
B) n
C) n - 1
D) None of these choices.

Accepted Answer

When the population standard deviation is unknown and we use the sample standard deviation to estimate it, the degrees of freedom for the test statistic for an F-test is given by (n-1). Therefore, the degrees of freedom for the test statistic for F1F1F1S1F1F1F10 when F1F1F1S1F1F1F10 is unknown is (n-1) for both the numerator and denominator of the F-test, giving a total of (n-1)+(n-1) = 2(n-1) degrees of freedom. This simplifies to n-2, which is equivalent to n F1F1F1S1F1F1F10 1. Thus, the correct answer is C.

Question 10

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 degrees of freedom for the t-distribution in this scenario are equal to n-1, where n is the sample size. We lose one degree of freedom by using the sample mean as an estimate of the population mean. This is because we used one piece of information (the sample mean) to estimate the population mean, and this reduces the total number of degrees of freedom in the sample.

Question 11

Researchers determined 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. Suppose the alternative we wanted to test was H₁: $\mu$ < 60. The correct rejection region for $\alpha$ = 0.05 is: A) reject H₀ if t > 1.6604. B) reject H₀ if t < -1.6604. C) reject H₀ if t > 1.9842 or Z < -1.9842. D) reject H₀ if t < -1.9842.

Accepted Answer

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

Question 12

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?
A) The population random variable must be normal.
B) The test statistic must be a non-negative number.
C) The test statistic must have a chi-squared distribution with n - 1 degrees of freedom.
D) All of these choices are true.

Accepted Answer

All of the choices are true regarding the chi-squared test statistic for the test of variance.

A) The population random variable does not need to be normal for the chi-squared test of variance. 
B) The test statistic must be a non-negative number because it is the sum of squared deviations, which are always non-negative. 
C) The test statistic must have a chi-squared distribution with n-1 degrees of freedom, where n is the sample size.

Question 13

The statistic (n - 1)s² / $\sigma$² has a chi-squared distribution with n - 1 degrees of freedom if: A) the sample has a Student t-distribution with degrees of freedom equal to n- 1. B) the sample is normally distributed with variance equal to s². C) the population is normally distributed with variance equal to $\sigma$². D) All of these choices are true.

Accepted Answer

The given statistic is the ratio of a sample mean (with sample size n) and a sample standard deviation (with sample size n-1) to the population standard deviation (which is unknown). This statistic follows a t-distribution, but as the sample size increases, the t-distribution approaches the normal distribution. Therefore, for large enough n, the statistic is approximately normally distributed. The variance of a normally distributed variable is its standard deviation squared. Thus, the variance of the given statistic is (s^2/n) / σ^2 where s^2 is the sample variance. Simplifying this expression yields s^2 / (nσ^2), which is equal to the population variance of the sample mean. Therefore, the given statistic has a chi-squared distribution with n-1 degrees of freedom if the underlying population is normally distributed with variance equal to σ^2. Thus, choice C is correct.

Question 14

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about $\mu$is the ____________________-distribution with ____________________ degrees of freedom.

Accepted Answer

The answer of When the population standard deviation is unknown...

Question 15

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 not sensitive to moderate nonnormality, meaning that it does not significantly change its value or behavior when the data deviates from a normal distribution. This type of estimator can handle outliers, skewness, and heavy tails in the data without compromising its accuracy or efficiency. While options A, B, and C all describe desirable properties for an estimator, they do not necessarily make it robust.

Question 16

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 17

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?
A) The population random variable must be normal.
B) The test statistic must be a non-negative number.
C) The test statistic must have a chi-squared distribution with n -1 degrees of freedom.
D) All of these choices are true.

Accepted Answer

All of the choices are true regarding the chi-squared test statistic for the test of variance. The population random variable does not need to be normal, but the test statistic must be non-negative and have a chi-squared distribution with n-1 degrees of freedom.

Question 18

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:
A) 19.353
B) 17.331
C) 17.110
D) 6.097

Accepted Answer

The answer of A random sample of 25 observations is...

Question 19

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

Using a t-table with 24 degrees of freedom (n-1), the critical value for a 99% confidence level is 2.7969.

Question 20

____________________ populations allow us to use the confidence interval estimate of a mean to produce a confidence interval estimate of the population total.

Accepted Answer

The answer of ____________________ populations allow us to use the...

Quiz 11: Inference About a Population

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

The t-test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n - 1 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:

Which of the following is not an example illustrating the use of variance?

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n - 1 degrees of freedom.

The degrees of freedom for the test statistic for $\mu$ when $\sigma$ is unknown is:

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:

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

The statistic (n - 1) s² / $\sigma$ ² has a chi-squared distribution with n - 1 degrees of freedom if:

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about $\mu$ is the -distribution with degrees of freedom.

A robust estimator is one that is:

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:

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:

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:

____________________ populations allow us to use the confidence interval estimate of a mean to produce a confidence interval estimate of the population total.

Quiz 11: Inference About a Population

When a population is small, we must adjust the test statistic and interval estimator using the ____________________ population correction factor.

The t-test for a population mean is ____________________, meaning that if the population is nonnormal, the results of the test and confidence interval are still valid as long as the nonnormality is not extreme.

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about μ\muμ is the t-distribution with n - 1 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:

Which of the following is not an example illustrating the use of variance?

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about μ\muμ is the t-distribution with n - 1 degrees of freedom.

The degrees of freedom for the test statistic for μ\muμ when σ\sigmaσ is unknown is:

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:

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

The statistic (n - 1) s2 / σ\sigmaσ 2 has a chi-squared distribution with n - 1 degrees of freedom if:

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about μ\muμ is the ____________________-distribution with ____________________ degrees of freedom.

A robust estimator is one that is:

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:

Which of the following conditions is needed regarding the chi-squared test statistic for the test of variance?

A random sample of 25 observations is selected from a normally distributed population. The sample variance is 10. In the 95% confidence interval for the population variance, the upper limit is:

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:

____________________ populations allow us to use the confidence interval estimate of a mean to produce a confidence interval estimate of the population total.

When the population standard deviation is ____________________ and the population is normal, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n - 1 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:

When the population standard deviation is unknown and the population is ____________________, the test statistic for testing hypotheses about $\mu$ is the t-distribution with n - 1 degrees of freedom.

The degrees of freedom for the test statistic for $\mu$ when $\sigma$ is unknown is:

The statistic (n - 1) s² / $\sigma$ ² has a chi-squared distribution with n - 1 degrees of freedom if:

When the population standard deviation is unknown and the population is normal, the test statistic for testing hypotheses about $\mu$ is the -distribution with degrees of freedom.