Question 1

In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is
A) a standard normal distribution.
B) a t distribution with 7 degrees of freedom.
C) a t distribution with 8 degrees of freedom.
D) a t distribution with 9 degrees of freedom.

Accepted Answer

When the population variance is unknown and the sample size is small (less than 30), we use the t distribution. Since we have 8 samples, we have 8-1 = 7 degrees of freedom, making choice B the best option. The standard normal distribution (choice A) is used when the population variance is known or the sample size is large (greater than 30), and choices C and D have too many and too few degrees of freedom, respectively.

Question 2

A recent study of 750 internet users in Europe found that 35% of internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the internet? A) B) C) D)

Accepted Answer

We can use the formula for the confidence interval of a proportion:

CI = p ± z*sqrt[p(1-p)/n]

where:
p = sample proportion = 0.35
n = sample size = 750
z = z-score for 95% confidence level = 1.96 (from standard normal distribution)

Plugging in the values:

CI = 0.35 ± 1.96*sqrt[0.35(1-0.35)/750]
CI = 0.35 ± 0.032
CI = (0.318, 0.382)

Therefore, the 95% confidence interval for the true proportion of women in Europe who use the internet is (0.318, 0.382). Choice C is the only one that matches this interval.

Question 3

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence. 
A) 
B) 
C) 
D)

Accepted Answer

The answer of The prices (in dollars) for a graphing...

Question 4

Find  when n = 23 for the 99% confidence interval for the mean.
A) 2.82
B) 2.51
C) 1.94
D) 3.46

Accepted Answer

The answer of Find  when n = 23 for...

Question 5

One of the characteristics of the t-distribution is that the curve never touches the ____-axis.

Accepted Answer

The answer of One of the characteristics of the t-distribution...

Question 6

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation for the population of 3.9 minutes. Jennifer's margin of error would be 1.4 minutes.

Accepted Answer

To calculate the margin of error for a 95% confidence interval, we use the formula:
Margin of error = 1.96 * (standard deviation/square root of sample size)

Plugging in the values given:
Margin of error = 1.96 * (3.9/square root of 30) = 1.4

Since the margin of error matches the value given in the question, we know that the answer is true.

Question 7

The _________________ are the number of values that are free to vary after a sample statistic has been computed.

Accepted Answer

The answer of The _________________ are the number of values...

Question 8

In a study of 100 new cars, 30 are white. Find  and  , where  is the proportion of new cars that are white.
A) 
B) 
C) 
D)

Accepted Answer

The answer of In a study of 100 new cars,...

Question 9

A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz., find the 95% confidence interval of the true mean.
A) 
B) 
C) 
D)

Accepted Answer

The answer of A food snack manufacturer samples 7 bags...

Question 10

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1500 pounds. At a 95% level, how many elephants need to be weighed so the average weight will be accurate to within 250 pounds?
A) 139
B) 165
C) 196
D) 324

Accepted Answer

The sample size needed to achieve the desired accuracy can be calculated using the formula:n = (Z^2 * s^2) / e^2where:n is the sample sizeZ is the z-score for the desired confidence levels is the standard deviation of the populatione is the margin of errorPlugging in the given values, we get:n = (1.96^2 * 1500^2) / 250^2n = 138.24Since we cannot have a fraction of an elephant, we round up to the nearest whole number, which is 139. Therefore, the correct answer is A) 139.

Question 11

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

Accepted Answer

The t-distribution can be used when the sample size is small (less than 30) and the variable is normally or approximately normally distributed. When the sample size is greater than 30, the t-distribution approaches the standard normal distribution, and it can be used if the variable is normally or approximately normally distributed.

Question 12

A study of nickels showed that the the standard deviation of the weight of nickels is 150 milligrams. A coin counter manufacturer wishes to find the 80% confidence interval for the average weight of a nickel. How many nickels does he need to weigh to obtain an average accurate to within 10 milligrams?
A) 225
B) 369
C) 613
D) 159

Accepted Answer

To find the sample size needed, we can use the formula:

n = (z*s / E)^2

where z is the z-score corresponding to the desired confidence level (80% = 1.28), s is the population standard deviation (150 mg), and E is the margin of error (10 mg).

Plugging in these values, we get:

n = (1.28*150 / 10)^2
n = 369

Therefore, the manufacturer needs to weigh at least 369 nickels to obtain an average accurate to within 10 milligrams with 80% confidence. So the correct choice is (B).

Question 13

The winning team's score in 7 high school basketball games was recorded. If the sample mean is 68.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean.
A) 
B) 
C) 
D)

Accepted Answer

Using the formula for a confidence interval:

CI = x̄ ± z*(σ/√n)

where x̄ = sample mean, σ = sample standard deviation, n = sample size, and z = z-score

We can solve for the interval using a z-table to find the z-score with a 98% confidence level, which is 2.33.

Plugging in the values:

CI = 68.3 ± 2.33*(13.0/√7)

CI = (50.7, 85.9)

Therefore, the 98% confidence interval of the true mean is (50.7, 85.9). Choice B is the correct answer.

Question 14

Identify the degree of confidence displayed in the confidence interval shown below. 
A) 90%
B) 95%
C) 98%
D) 99%

Accepted Answer

The answer of Identify the degree of confidence displayed in...

Question 15

What is the value of $\alpha$ used in describing the confidence interval shown below. 
A) 0.01
B) 0.02
C) 0.04
D) 0.05

Accepted Answer

The answer of What is the value of $\alpha$ used...

Question 16

The t-distribution has a variance that is greater than one.

Accepted Answer

The t-distribution has a variance that is greater than one, which is why it has fatter tails than the normal distribution.

Question 17

The value of used in the figure below is 0.02.

Accepted Answer

The answer of The value of used...

Question 18

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 15 millimeters. A packer wishes to find the 90% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 3 millimeters?
A) 25
B) 97
C) 69
D) 41

Accepted Answer

The formula for the sample size needed for a confidence interval is:
n = (z * σ / E)^2
Where n is the sample size, z is the z-score for the desired confidence interval (1.645 for 90% confidence), σ is the population standard deviation (given as 15 millimeters), and E is the margin of error desired (3 millimeters).

Plugging these values into the formula, we get:
n = (1.645 * 15 / 3)^2
n = 68.6

Since we cannot have a fraction of a box, we round up to the nearest whole number:
n = 69

Therefore, the packer needs to measure 69 boxes to be accurate within 3 millimeters with 90% confidence. The answer is C) 69.

Question 19

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 20. If he were to conduct a second study to reduce the maximum error of estimate to 5, about how many hard drives should he include in his new sample?
A) 45
B) 90
C) 180
D) 720

Accepted Answer

To reduce the maximum error of estimate by a factor of 4 (from 20 to 5), the sample size must be increased by a factor of 16 (since error is inversely proportional to the square root of the sample size). Thus, 45 * 16 = 720.

Question 20

3 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.
A) 
B) 
C) 
D)

Accepted Answer

The answer of 3 squirrels were found to have an...

Quiz 7: Confidence Intervals and Sample Size

In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is

A recent study of 750 internet users in Europe found that 35% of internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the internet?

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence.

Find when n = 23 for the 99% confidence interval for the mean.

One of the characteristics of the t-distribution is that the curve never touches the ____-axis.

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation for the population of 3.9 minutes. Jennifer's margin of error would be 1.4 minutes.

The _________________ are the number of values that are free to vary after a sample statistic has been computed.

In a study of 100 new cars, 30 are white. Find and , where is the proportion of new cars that are white.

A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz., find the 95% confidence interval of the true mean.

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1500 pounds. At a 95% level, how many elephants need to be weighed so the average weight will be accurate to within 250 pounds?

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

The winning team's score in 7 high school basketball games was recorded. If the sample mean is 68.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean.

Identify the degree of confidence displayed in the confidence interval shown below.

What is the value of $\alpha$ used in describing the confidence interval shown below. $What is the value of \alpha used in describing the confidence interval shown below. A) 0.01 B) 0.02 C) 0.04 D) 0.05$

The t-distribution has a variance that is greater than one.

The value of used in the figure below is 0.02.

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 15 millimeters. A packer wishes to find the 90% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 3 millimeters?

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 20. If he were to conduct a second study to reduce the maximum error of estimate to 5, about how many hard drives should he include in his new sample?

3 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.

Quiz 7: Confidence Intervals and Sample Size

In a study using 8 samples, and in which the population variance is unknown, the distribution that should be used to calculate confidence intervals is

A recent study of 750 internet users in Europe found that 35% of internet users were women. What is the 95% confidence interval of the true proportion of women in Europe who use the internet?

The prices (in dollars) for a graphing calculator are shown below for 8 online vendors. Estimate the true mean price for this particular calculator with 95% confidence.

Find when n = 23 for the 99% confidence interval for the mean.

One of the characteristics of the t-distribution is that the curve never touches the ____-axis.

Jennifer wants to find a 95% confidence interval for the time it takes her to get to work. She kept records for 30 days and found her average time to commute to work was 20.5 minutes with a standard deviation for the population of 3.9 minutes. Jennifer's margin of error would be 1.4 minutes.

The _________________ are the number of values that are free to vary after a sample statistic has been computed.

In a study of 100 new cars, 30 are white. Find and , where is the proportion of new cars that are white.

A food snack manufacturer samples 7 bags of pretzels off the assembly line and weighs their contents. If the sample mean is 14.2 oz. and the sample standard deviation is 0.60 oz., find the 95% confidence interval of the true mean.

A study of elephants is conducted to determine the average weight of a certain subspecies of elephants. The standard deviation for the population is 1500 pounds. At a 95% level, how many elephants need to be weighed so the average weight will be accurate to within 250 pounds?

The t-distribution must be used when the sample size is greater than 30 and the variable is normally or approximately normally distributed.

The winning team's score in 7 high school basketball games was recorded. If the sample mean is 68.3 points and the sample standard deviation is 13.0 points, find the 98% confidence interval of the true mean.

Identify the degree of confidence displayed in the confidence interval shown below.

What is the value of α\alphaα used in describing the confidence interval shown below.

The t-distribution has a variance that is greater than one.

The value of used in the figure below is 0.02.

A previous analysis of paper boxes showed that the the standard deviation of their lengths is 15 millimeters. A packer wishes to find the 90% confidence interval for the average length of a box. How many boxes does he need to measure to be accurate within 3 millimeters?

A researcher conducted a study of the access speed of 45 hard drives and concluded that his maximum error of estimate was 20. If he were to conduct a second study to reduce the maximum error of estimate to 5, about how many hard drives should he include in his new sample?

3 squirrels were found to have an average weight of 9.3 ounces with a sample standard deviation is 1.1. Find the 95% confidence interval of the true mean weight.

What is the value of $\alpha$ used in describing the confidence interval shown below. $What is the value of \alpha used in describing the confidence interval shown below. A) 0.01 B) 0.02 C) 0.04 D) 0.05$