Question 1

Use the following information for questions:
 For each study, decide if the two samples are independent samples or paired samples.
-A group of 50 students each measured the length of their right arm and the length of their left arm. The average right arm lengths were compared to the average left arm lengths.
A) Independent samples
B) Paired samples

Accepted Answer

Each student's right arm length is naturally paired with their left arm length, making the samples paired since measurements are taken from the same individual.

Question 2

Use the following information for questions:
 For each study, decide if the two samples are independent samples or paired samples.
-A study compared the average number of courses taken by a random sample of 100 freshmen at a university with the average number of courses taken by a separate random sample of 50 freshmen at a community college.
A) Independent samples
B) Paired samples

Accepted Answer

The two samples are from different populations (university freshmen vs. community college freshmen) and are selected independently of each other, making them independent samples.

Question 3

Use the following information for questions:
 For each study, decide if the two samples are independent samples or paired samples.
-A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students). The groups were followed for 2 weeks and the proportions of students with colds were compared.
A) Independent samples
B) Paired samples

Accepted Answer

The two groups (vitamin C and placebo) are separate and do not have any inherent pairing or matching between the individuals in one group to those in the other, making them independent samples.

Question 4

Use the following information for questions:
 For each study, decide if the two samples are independent samples or paired samples.
-A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.
A) Independent samples
B) Paired samples

Accepted Answer

The same group of students had their blood pressures measured before and after watching a movie, making the samples paired because measurements are taken from the same subjects at two different times.

Question 5

Which of the following helps determine the standard error for a confidence interval for a mean?
A) The sample size(s).
B) The sample estimate.
C) The true value of the population parameter.
D) The confidence level.

Accepted Answer

The standard error for a confidence interval for a mean is calculated using the sample size and the sample standard deviation. The sample size directly affects the standard error, as it is inversely proportional to the square root of the sample size.

Question 6

The distinction between a sampling distribution and a confidence interval is:
A) A confidence interval gives possible values for a sample statistic when the population parameter is assumed known, while a sampling distribution gives possible values for a population parameter when only a single value of a sample statistic is known.
B) A sampling distribution gives possible values for a sample statistic when the population parameter is assumed known, while a confidence interval gives possible values for a population parameter when only a single value of a sample statistic is known.
C) Sampling distributions exist only for situations involving means, while confidence intervals can be computed for situations involving means and proportions.
D) Confidence intervals exist only for situations involving means, while sampling distributions can be computed for situations involving means and proportions.

Accepted Answer

A sampling distribution describes the distribution of a sample statistic over many samples drawn from the same population, showing how that statistic varies. A confidence interval, on the other hand, uses a single sample statistic to estimate a range of plausible values for a population parameter, incorporating the uncertainty of that estimate.

Question 7

A randomly selected sample of 100 students had an average grade point average (GPA) of 3.2 with a standard deviation of 0.2. The standard error of the sample mean is
A) 0.020
B) 0.200
C) 1.600
D) 2.000

Accepted Answer

The answer of A randomly selected sample of 100 students...

Question 8

A randomly selected sample of 30 students spent an average amount of $40.00 on a date, with a standard deviation of $5.00. The standard error of the sample mean is
A) 0.063
B) 0.167
C) 0.913
D) 5.000

Accepted Answer

The answer of A randomly selected sample of 30 students...

Question 9

A random sample of 250 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the standard error of the sample mean?
A) 0.95
B) 0.202
C) 0.0038
D) 0.060

Accepted Answer

The standard error of the sample mean is calculated by dividing the standard deviation by the square root of the sample size: SE = 0.95 / √250 ≈ 0.060.

Question 10

A randomly selected sample of 60 mathematics majors spent an average of $200.00 for textbooks one term, while during the same term, a randomly selected sample of 40 literature majors spent an average of $180.00 for textbooks. The standard deviation for each sample was $20.00. The standard error for the difference between the two sample means is
A) 0.057
B) 4.082
C) 5.744
D) 16.663

Accepted Answer

The standard error for the difference between two sample means is calculated using the formula: $\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}$, where $s_1$ and $s_2$ are the standard deviations of the two samples, and $n_1$ and $n_2$ are the sample sizes. Substituting the given values ($s_1 = s_2 = 20$, $n_1 = 60$, $n_2 = 40$), we get $\sqrt{\frac{20^2}{60} + \frac{20^2}{40}} = \sqrt{\frac{400}{60} + \frac{400}{40}} = \sqrt{6.67 + 10} = \sqrt{16.67} \approx 4.082$.

Question 11

A random sample of 40 men drank an average of 20 cups of coffee per week during finals, while a sample of 30 women drank an average of 15 cups of coffee per week. The sample standard deviations were 6 cups for the men and 3 cups for the women. The standard error for the difference between the two sample means is
A) 1.095
B) 1.200
C) 1.549
D) 2.400

Accepted Answer

The standard error for the difference between two sample means is calculated using the formula: SE = sqrt((s1^2/n1) + (s2^2/n2)), where s1 and s2 are the standard deviations, and n1 and n2 are the sample sizes. Plugging in the values: SE = sqrt((6^2/40) + (3^2/30)) = sqrt((36/40) + (9/30)) = sqrt(0.9 + 0.3) = sqrt(1.2) = 1.095.

Question 12

Conscientiousness is a tendency to show self-discipline, act dutifully, and aim for achievement. The trait shows a preference for planned rather than spontaneous behavior. A random sample of 650 students is asked to fill out the Hogan Personality Inventory (HPI) to measure their level of conscientiousness. The 300 undergraduate students scored an average of 145 with a standard deviation of 16. The 350 graduate students had a mean score of 153 with a standard deviation of 21. What is the standard error for the difference between the two sample means?
A) 18.5
B) 2.11
C) 1.45
D) 2.05

Accepted Answer

The answer of Conscientiousness is a tendency to show self-discipline,...

Question 13

Which of the following is not true about the standard error of a statistic?
A) The standard error measures, roughly, the average difference between the statistic and the population parameter.
B) The standard error is the estimated standard deviation of the sampling distribution for the statistic.
C) The standard error can never be a negative number.
D) The standard error increases as the sample size(s) increases.

Accepted Answer

The standard error decreases as the sample size increases, because larger samples tend to be more representative of the population, thus reducing the variability of the statistic.

Question 14

For a randomly selected sample of n = 36 men's heights, it is reported that the standard error of the mean is 0.5 inches. Three of the following statements are true, while one is false. Which statement is false?
A) The standard error (0.5 inches) is an estimated value of the standard deviation of the sample mean.
B) If a new sample of n = 36 men's heights is collected, the standard error of the mean might not equal 0.5 inches.
C) Over many different samples of n = 36 men's heights, the average difference between the sample mean and population mean will be roughly 0.5 inches.
D) In about 95% of all samples of n = 36 men's heights, the sample mean will be within 0.5 inches of the population mean.

Accepted Answer

The standard error of 0.5 inches indicates the standard deviation of the sample mean distribution, not the range within which 95% of sample means will fall. The 95% confidence interval would be wider, typically 1.96 times the standard error.

Question 15

What is the primary purpose of a 95% confidence interval for a mean?
A) to estimate a sample mean
B) to test a hypothesis about a sample mean
C) to estimate a population mean
D) to provide an interval that covers 95% of the individual values in the population

Accepted Answer

The primary purpose of a 95% confidence interval for a mean is to estimate a population mean, indicating the range within which the true population mean is likely to fall with 95% confidence.

Question 16

The confidence level for a confidence interval for a mean is
A) the probability the procedure provides an interval that covers the sample mean.
B) the probability of making a Type 1 error if the interval is used to test a null hypothesis about the population mean.
C) the probability that individuals in the population have values that fall into the interval.
D) the probability the procedure provides an interval that covers the population mean.

Accepted Answer

The confidence level for a confidence interval for a mean indicates the probability that the interval estimation procedure will produce an interval that captures the true population mean.

Question 17

Which of the following will not result in paired data?
A) The same measurement is taken twice on each person, under different conditions or at different times.
B) Similar individuals are paired before giving the treatments in an experiment. Each member of a pair then receives a different treatment. The same response variable is measured for all individuals.
C) Two different variables are measured for each individual. There is interest in the amount of difference between the two variables.
D) One random sample is taken, and a variable is recorded for each individual, but then units are categorized as belonging to one population or another.

Accepted Answer

Paired data typically involve measurements taken on the same subject under different conditions or two subjects matched in some way. Choice D describes taking a single measurement on each individual and then categorizing them, which does not involve pairing in the same sense as the other options.

Question 18

Which of the following statements is most correct about a confidence interval for a mean?
A) It provides a range of values, any of which is a good guess at the possible value of the sample mean.
B) It provides a range of values, any of which is a good guess at the possible value of the population mean.
C) It provides a good guess for the range of values the sample mean is likely to have in repeated samples.
D) It provides a good guess for the range of values the population mean is likely to have in repeated samples.

Accepted Answer

A confidence interval for a mean provides a range of values within which we can be confident the population mean lies, not the sample mean.

Question 19

The weights of a sample of n = 8 college men will be used to create a 95% confidence interval for the mean weight of all college men. What is the correct t* multiplier involved in calculating the interval?
A) 1.89
B) 2.00
C) 2.31
D) 2.36

Accepted Answer

The correct t* multiplier for a 95% confidence interval with 8 degrees of freedom is 2.36.

Question 20

The heights of a sample of n = 18 female college students will be used to create a 98% confidence interval for the mean height of all female college students. What is the correct t* multiplier for this interval?
A) 2.11
B) 2.55
C) 2.57
D) 2.90

Accepted Answer

The correct t* multiplier for a 98% confidence interval with n = 18 (degrees of freedom = 17) is approximately 2.57, based on the t-distribution table or calculator.

Quiz 11: Estimating Means With Confidence

Which of the following helps determine the standard error for a confidence interval for a mean?

The distinction between a sampling distribution and a confidence interval is:

A randomly selected sample of 100 students had an average grade point average (GPA) of 3.2 with a standard deviation of 0.2. The standard error of the sample mean is

A randomly selected sample of 30 students spent an average amount of $40.00 on a date, with a standard deviation of $5.00. The standard error of the sample mean is

A random sample of 250 third graders scored an average of 3.2 on a standardized reading test. The standard deviation was 0.95. What is the standard error of the sample mean?

Which of the following is not true about the standard error of a statistic?

For a randomly selected sample of n = 36 men's heights, it is reported that the standard error of the mean is 0.5 inches. Three of the following statements are true, while one is false. Which statement is false?

What is the primary purpose of a 95% confidence interval for a mean?

The confidence level for a confidence interval for a mean is

Which of the following will not result in paired data?

Which of the following statements is most correct about a confidence interval for a mean?

The weights of a sample of n = 8 college men will be used to create a 95% confidence interval for the mean weight of all college men. What is the correct t* multiplier involved in calculating the interval?

The heights of a sample of n = 18 female college students will be used to create a 98% confidence interval for the mean height of all female college students. What is the correct t* multiplier for this interval?