Question 1

Determine the critical value  that corresponds to the given level of confidence.
-92%
A) 1.41
B) 0.82
C) 1.45
D) 1.75

Accepted Answer

D

Question 2

Determine the critical value  that corresponds to the given level of confidence.
-97%
A) 1.88
B) 1.92
C) 2.17
D) 0.83

Accepted Answer

The z-score corresponding to a 97% confidence level is approximately 2.17.

Question 3

An article a Florida newspaper reported on the topics that teenagers most want to discuss with their parents. The findings, the results of a poll, showed that 46% would like more discussion about the family's financial situation, 37% would like to talk about school, and 30% would like to talk about religion. These and other percentages were based on a national sampling of 535 teenagers. Estimate the proportion of all teenagers who want more family discussions about school. Use a 99% confidence level. Express the answer in the form  ± E and round to the nearest thousandth.
A) 0.37 ± 0.0 54
B) 0.37 ± 0.00 2
C) 0.63 ± 0.00 2
D) 0.63 ± 0.0 54

Accepted Answer

A

Question 4

The general form of a large-sample (1 - ?) 100% confidence interval for a population proportion p is  where  =  is the sample proportion of observations with the characteristic of interest.

Accepted Answer

The answer of The general form of a large-sample (1...

Question 5

What is the best point estimate for p in order to construct a confidence interval for p?
A) 
B) 
C) 
D)

Accepted Answer

The answer of What is the best point estimate for...

Question 6

A confidence interval for p can be constructed using
A)  ±z 
B)  ±  
C) p ± z 
D) p ±

Accepted Answer

The answer of A confidence interval for p can be...

Question 7

A local outdoor equipment store is being sold. The buyers are trying to estimate the percentage of items that are outdated. They will randomly sample among its 100,000 items in order to determine the proportion of merchandise that is outdated. The current owners have never determined their outdated percentage and can not help the buyers. Approximately how large a sample do the buyers need in order to insure that they are 98% confident that the margin of error is within 3%?
A) 1509
B) 648
C) 6033
D) 3017

Accepted Answer

To ensure a 98% confidence level with a margin of error within 3%, the sample size can be calculated using the formula for sample size in estimating proportions: $n = \frac{Z^2 \cdot p \cdot (1-p)}{E^2}$, where $Z$ is the Z-score corresponding to the confidence level (approximately 2.33 for 98%), $p$ is the estimated proportion (0.5 is used when the proportion is unknown for maximum sample size), and $E$ is the margin of error (0.03 for 3%). Plugging in the values: $n = \frac{2.33^2 \cdot 0.5 \cdot (1-0.5)}{0.03^2}$, which simplifies to approximately 1509. This is the sample size needed to achieve the desired confidence level and margin of error.

Question 8

When choosing the sample size for estimating a population proportion p to within E units with confidence  if you take  as the approximation to p, you will always obtain a sample size that is at least as large as required.

Accepted Answer

The answer of When choosing the sample size for estimating...

Question 9

Determine the point estimate of the population mean and margin of error for the confidence interval with lower bound 18 and upper bound: 32.
A)  =18, E=14
B)  =32, E=7
C)  =25, E=14
D)  =25, E=7

Accepted Answer

The answer of Determine the point estimate of the population...

Question 10

A simple random sample of size n < 30 for a quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected z-score, and the boxplot, judge whether a t-interval should be constructed.
-n = 14; Correlation = 0.956

Accepted Answer

The answer of A simple random sample of size n...

Question 11

A simple random sample of size n < 30 for a quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected z-score, and the boxplot, judge whether a t-interval should be constructed.
-n = 10; Correlation = 0.896

Accepted Answer

The answer of A simple random sample of size n...

Question 12

Suppose a 99% confidence interval for ? turns out to be (1000,2100) .If this interval was based on a sample of size n=23,explain what assumptions are necessary for this interval to be valid.
A) The sampling distribution of the sample mean must have a normal distribution.
B) The sampling distribution must be biased with 22 degrees of freedom.
C) The population of salaries must have an approximate t distribution.
D) The population must have an approximately normal distribution.

Accepted Answer

The assumption necessary for the confidence interval to be valid is that the population from which the sample is drawn must have an approximately normal distribution, especially given the small sample size (n=23).

Question 13

A computer package was used to generate the following printout for estimating the sale price of condominiums in a particular neighborhood.  What assumptions are necessary for any inferences derived from this printout to be valid?
A) The population mean has an approximate normal distribution.
B) The sample variance equals the population variance.
C) The sample was randomly selected from an approximately normal population.
D) All of these are necessary.

Accepted Answer

The answer of A computer package was used to generate...

Question 14

Find the t-value.
-Let  be a specific value of t. Find  such that the statement is true: P(t ?  ) = 0 .1 where df = 20.
A) -1.328
B) 1.325
C) 1.328
D) -1.325

Accepted Answer

The answer of Find the t-value.
-Let  be a specific...

Question 15

Find the t-value.
-Find the t-value such that the area in the right tail is 0.05 with 34 degrees of freedom.
A) 2.728
B) -1.691
C) 1.691
D) 1.694

Accepted Answer

For a t-distribution with 34 degrees of freedom, the t-value that leaves an area of 0.05 in the right tail is approximately 1.691.

Question 16

Find the t-value.
-Find the t-value such that the area left of the t-value is 0.025 with 17 degrees of freedom.
A) -2.11
B) -3.222
C) 2.120
D) 2.110

Accepted Answer

The t-value that leaves an area of 0.025 to the left with 17 degrees of freedom is found using a t-distribution table or calculator. The negative sign indicates it's to the left of the mean. The correct value is approximately -2.11.

Question 17

In a random sample of 26 laptop computers, the mean repair cost was $131 with a standard deviation of $38. Assume the population has a normal distribution. Construct a 95% confidence interval for the population mean, ?. Suppose you did some research on repair costs for laptop computers and found that the standard deviation is  . Use the normal distribution to construct a 95% confidence interval for the population mean, ?. Compare the results. Round to the nearest cent.

Accepted Answer

The answer of In a random sample of 26 laptop...

Question 18

In order to set rates, an insurance company is trying to estimate the number of sick days that full time workers at a local bank take per year. Based on earlier studies, they will assumed that s= 2.2 days 
a) How large a sample must be selected if the company wants to be 98% confident that their estimate is within 1 day of the true mean?
b) Repeat part (a) using a 99% confidence interval. Which level of confidence requires a larger sample size? Explain.

Accepted Answer

The answer of In order to set rates, an insurance...

Question 19

In a random sample of 60 dog owners enrolled in obedience training, it was determined that the mean amount of money spent per owner was $109.33 per class. Assuming the population standard deviation of the amount spent per owner is $12, construct and interpret a 95% confidence interval for the mean amount spent per owner for an obedience class.
A) ($106.23, $112.43); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $106.23 and $112.43.
B) ($106.29, $112.37); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $106.29 and $112.37.
C) ($106.74, $111.92); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $106.74 and $111.92.
D) ($106.78, $111.88); we are 95% confident that the mean amount spent per dog owner for a single obedience class is between $106.78 and $111.88.

Accepted Answer

The answer of In a random sample of 60 dog...

Question 20

A survey of 1010 college seniors working towards an undergraduate degree was conducted. Each student was asked, "Are you planning or not planning to pursue a graduate degree?" Of the 1010 surveyed, 658 stated that they were planning to pursue a graduate degree. Construct and interpret a 98% confidence interval for the proportion of college seniors who are planning to pursue a graduate degree.
A) (0.616, 0.686); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.616 and 0.686.
B) (0.621, 0.680); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.621 and 0.680.
C) (0.612, 0.690); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.612 and 0.690.
D) (0.620, 0.682); we are 98% confident that the proportion of college seniors who are planning to pursue a graduate degree is between 0.620 and 0.682.

Accepted Answer

The correct confidence interval is calculated using the sample proportion (p̂ = 658/1010), the z-score for a 98% confidence level, and the formula for the confidence interval of a proportion. The interval (0.616, 0.686) accurately reflects the calculation and interpretation for this scenario.

Quiz 9: Estimating the Value of a Parameter Using Confidence Intervals

Determine the critical value that corresponds to the given level of confidence. -92%

Determine the critical value that corresponds to the given level of confidence. -97%

The general form of a large-sample (1 - ?) 100% confidence interval for a population proportion p is where = is the sample proportion of observations with the characteristic of interest.

What is the best point estimate for p in order to construct a confidence interval for p?

A confidence interval for p can be constructed using

When choosing the sample size for estimating a population proportion p to within E units with confidence if you take as the approximation to p, you will always obtain a sample size that is at least as large as required.

Determine the point estimate of the population mean and margin of error for the confidence interval with lower bound 18 and upper bound: 32.

A simple random sample of size n < 30 for a quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected z-score, and the boxplot, judge whether a t-interval should be constructed. -n = 14; Correlation = 0.956

A simple random sample of size n < 30 for a quantitative variable has been obtained. Using the normal probability plot, the correlation between the variable and expected z-score, and the boxplot, judge whether a t-interval should be constructed. -n = 10; Correlation = 0.896

Suppose a 99% confidence interval for ? turns out to be (1000,2100) .If this interval was based on a sample of size n=23,explain what assumptions are necessary for this interval to be valid.

A computer package was used to generate the following printout for estimating the sale price of condominiums in a particular neighborhood. What assumptions are necessary for any inferences derived from this printout to be valid?

Find the t-value. -Let be a specific value of t. Find such that the statement is true: P(t ? ) = 0 .1 where df = 20.

Find the t-value. -Find the t-value such that the area in the right tail is 0.05 with 34 degrees of freedom.

Find the t-value. -Find the t-value such that the area left of the t-value is 0.025 with 17 degrees of freedom.