Question 1

The scores of individual students on the American College Testing (ACT),a college readiness assessment,have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0.At Northside High,36 seniors take the test.Assume the scores at this school have the same distribution as national scores.What is the sampling distribution of the sample mean score for a random sample of 36 students?
A)Approximately Normal,but the approximation is poor
B)Approximately Normal,and the approximation is good
C)Exactly Normal
D)Neither Normal nor non-Normal-it depends on the particular 36 students selected

Accepted Answer

The answer of The scores of individual students on the...

Question 2

The proportion of supermarket customers who do not buy store-brand products is to be estimated.Which of the following scenarios would lead to a sampling distribution of the sample proportion with the lowest variability?
A)Sample 100 customers from the roughly 2000 customers who shop at one store location.
B)Sample 100 customers from the roughly 20,000 customers who shop at the stores citywide.
C)Sample 200 customers from the roughly 2000 customers who shop at one store location.
D)Sample 300 customers from the roughly 20,000 customers who shop at the stores citywide.

Accepted Answer

Sampling a larger number of customers (300) from a larger population (roughly 20,000) leads to a sampling distribution of the sample proportion with the lowest variability because larger sample sizes generally result in lower variability in the sampling distribution.

Question 3

Which histograms display a sampling distribution that is unbiased for estimating the proportion of women at a large university,which is known to be 45%?
A) 
B) 
C) 
D)

Accepted Answer

The answer of Which histograms display a sampling distribution that...

Question 4

For the following scenario,determine if the numbers in boldface type are statistics or parameters. A company manufactures cardboard containers for packaging frozen fruit juices.The manufacturing process forms the containers by joining cardboard stock to a metal bottom.The container can be inspected to determine if there might be leaks along the cardboard seam or where the metal bottom is attached.It is known from long experience that 18% of cans produced by this process are defective.A random sample of 50 cans was selected from the production process on Monday,and it was found that 12% of the selected cans were defective.Because this seemed to indicate an improvement,another sample was selected of the same size on Tuesday,and in it 21% of the cans were defective.The numbers 12%,18%,and 21% are,respectively,a
A)statistic,statistic,and parameter.
B)statistic,statistic,and statistic.
C)parameter,statistic,and parameter.
D)parameter,parameter,and statistic.
E)statistic,parameter,and statistic.

Accepted Answer

The 18% is a parameter because it represents the long-term average (or the whole population) of defective cans produced by the process. The 12% and 21% are statistics because they are derived from samples taken on Monday and Tuesday, respectively.

Question 5

The proportion of supermarket customers who do not buy store-brand products is to be estimated.Suppose 500 customers are selected from the roughly 20,000 customers who shop at the stores citywide.The sample proportion of supermarket customers who do not buy store-brand products equals 33.5%.Which value(s)can be labeled as statistic(s)?
A)20,000
B)500 and 20,000
C)33.5%
D)20,000 and 33.5%

Accepted Answer

The sample proportion of 33.5% is a statistic because it is a numerical summary of the sample data. The population size of 20,000 and the sample size of 500 are population parameters, not statistics.

Question 6

The scores of individual students on the American College Testing (ACT),college readiness assessment,have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0.At Northside High,36 seniors take the test.Assume the scores at this school have the same distribution as national scores.What is the mean of the sampling distribution of the sample mean score for a random sample of 36 students?
A)1.0
B)3.1
C)6.0
D)18.6

Accepted Answer

The mean of the sampling distribution of the sample mean score for a random sample of 36 students is equal to the population mean, which is 18.6. Therefore, the correct choice is D.

Question 7

Hoping to attract more shoppers,a city is planning to build a new public parking garage downtown.The city plans to pay for the structure through parking fees.The consultant,who is advising the city on this project,has selected a simple random sample of 44 weekdays and calculated the average amount in fees collected from neighboring parking structures.The sample mean was $967.Which of the following scenarios would lead to the smallest margin of error?
A)Sample fewer days,so that the sample mean may be lower than $967 and the margin of error will be smaller as well.
B)Sample fewer days-a smaller sample size will automatically lead to a smaller margin of error.
C)Sample more days-with more days we have more data and our estimate is expected to be more accurate,leading to a smaller margin of error.
D)Stay with a sample size of 44 days-this sample size was used for a reason,which was most likely to reduce the margin of error.

Accepted Answer

Sampling more days increases the sample size, which generally leads to a more accurate estimate of the population mean. This accuracy is reflected in a smaller margin of error, as the estimate is based on more data points, making it more reliable.

Question 8

Which of the following statements best describes a sampling distribution?
A)It is the distribution of the values of a particular variable that are observed in a random sample.
B)It is the distribution of the values of a variable in the population from which the sample is taken.
C)It is the distribution of the values of a statistic calculated from 1000 simple random samples displayed in a histogram.
D)It is the distribution of the values of a statistic that resembles the Normal distribution when the sample size is large.
E)It is the distribution of the values taken by a statistic in all possible samples of the same size from the same population.

Accepted Answer

The answer of Which of the following statements best describes...

Question 9

Every year around Christmas time,many parents take their children to a mall to have their child's picture taken with Santa.The Centennial Mall management has calculated,based on years of experience,that about 40% of all children cry when they sit on Santa's lap.Suppose 80 children were randomly selected from this year's crowd.Of these 80 children,45% cried.If repeated samples of 80 children were to be selected,what is the center of the sampling distribution of the percentage of sampled children who cry when seated on Santa's lap?
A)40%
B)45%
C)80
D)Somewhere between 40% and 45%

Accepted Answer

The center of the sampling distribution of the percentage of sampled children who cry when seated on Santa's lap is equal to the population proportion, which is 40%.

Question 10

A simple random sample of 50 students is taken from a local community college,which has a total of about 1500 students.Another simple random sample of 50 students is taken from a large state university,which has a total of approximately 20,000 students.The sampled students each answer a one-question survey which reads,"About how many MP3 songs do you own?" The sample average number of MP3 songs owned is calculated for the two sets of students.What can we conclude about the sampling variability in the sample average number of MP3 songs of the students sampled from the small community college as compared to that in the sample average of the students sampled from the large state university?
A)The sample mean from the small community college has less sampling variability than that from the large state university because there are fewer students at the small community college.
B)The sample mean from the small community college has more sampling variability than that from the large state university because there are more students at the large state university.
C)The sample mean from the small community college has about the same sampling variability as that from the large state university because the sample sizes are equal.
D)It is impossible to make any statements about the sampling variability of the two sample means because the students surveyed came from different schools.

Accepted Answer

The sampling variability is primarily determined by the sample size, not the population size, as long as the population is sufficiently large. Since both samples are of equal size (50 students each), the sampling variability in the sample averages should be about the same, regardless of the total number of students at each institution.

Question 11

The scores of individual students on the American College Testing (ACT),college readiness assessment,have a Normal distribution with a mean of 18.6 and a standard deviation of 6.0.At Northside High,36 seniors take the test.Assume the scores at this school have the same distribution as national scores.What is the standard deviation of the sampling distribution of the sample mean score for a random sample of 36 students?
A)1.0
B)3.1
C)6.0
D)18.6

Accepted Answer

The standard deviation of the sampling distribution of the sample mean (often called the standard error) is equal to the population standard deviation divided by the square root of the sample size. Here, it is 6.0 / sqrt(36) = 6.0 / 6 = 1.0.

Question 12

The number of undergraduates at Johns Hopkins University is approximately 2000,while the number at Ohio State University is approximately 40,000.Suppose the actual proportion of undergraduates at Johns Hopkins University who feel drinking is a problem among college students is 67%.What is the mean of the sampling distribution of the percentage of students who feel drinking is a problem in repeated simple random samples of 50 Johns Hopkins undergraduates?
A)60%
B)65%
C)67%
D)70%

Accepted Answer

The mean of the sampling distribution of the percentage of students who feel drinking is a problem in repeated simple random samples is equal to the actual proportion of undergraduates who feel drinking is a problem, which is given as 67%. Therefore, the answer is C) 67%.

Question 13

Consider a Poisson distribution with a mean of 4.What is the probability that X < 3?
A).238
B)0
C).433
D)None of the above

Accepted Answer

The probability that X < 3 in a Poisson distribution with a mean of 4 can be calculated using the Poisson probability formula for X = 0, 1, and 2, and then summing these probabilities. The correct calculation leads to a value close to 0.238, making option A the correct choice.

Question 14

A population of graduate students at a large university was being studied through the use of a sample survey.The researcher was trying to estimate the mean debt carried by the students through student loans and the proportion of all students that carry a student loan.A stratified random sample of 350 students was selected from the various schools within the university.The sample results showed that 30% held a student loan and the mean debt was $18,450.Which of the following statements is TRUE?
A)The result,30%,is a statistic and the mean debt,$18,450,is the value of the parameter.
B)The mean debt held by all students is a parameter,and the 30% who hold student loans is the value of a parameter.
C)The mean debt of all students,the proportion holding a loan,and the values 30% and $18,450 are all examples of parameters.
D)The mean debt of all students and the proportion holding student loans are both parameters,but the values 30% and $18,450 are statistics.
E)The mean debt of all students is a parameter,and its value is $18,450.The proportion holding a student loan is also a parameter whose value is 30%.

Accepted Answer

Parameters refer to the characteristics of the entire population, while statistics are derived from samples. The mean debt and the proportion of students holding loans for the entire population are parameters. The specific values of 30% and $18,450, obtained from the sample, are statistics.

Question 15

The figure below shows the Poisson distribution with a mean of 4.The Poisson distribution is an example of _________. 
A)continuous probability distribution
B)discrete probability distribution

Accepted Answer

The Poisson distribution is a discrete probability distribution, which models the number of events occurring in a fixed interval of time or space.

Question 16

Should you have a cup of coffee to make you more alert when studying for a big test? A study on the effect of caffeine involved asking volunteers to take a memory test 20 minutes after drinking cola.Some volunteers were randomly assigned to drink caffeine-free cola,some were assigned regular cola (with caffeine),and others were assigned a mixture of the two (getting a half dose of caffeine).For each volunteer,a test score (the number of items recalled correctly)was recorded.The volunteers were not told which type of cola they had been given,but the researchers for the study prepared the cups of cola right on the spot (out of sight of the volunteers).The memory test had a total of 25 items on it.The average number of items recalled was 15 for the caffeine-free group,17 for the mixture group,and 16 for the regular cola group.Are the values 15,16,and 17 statistics or parameters?

Accepted Answer

The answer of Should you have a cup of coffee...

Question 17

A news program is doing a report on a controversial court case.Daniel VanHowen is being prosecuted for killing a woman in the park,but all the evidence is circumstantial.Right before sentencing,the TV program decides to poll the TV-viewing audience.They wish to estimate the proportion of all people who think Mr.VanHowen is guilty.They decide to post a question on their Web site and ask the TV-viewing audience to answer it.The TV program decides to announce during the program that these opinions only reflect the TV-viewing,computer-using audience.They close the poll after 10 minutes.They had 2371 responses,of which 1542 think that Mr.VanHowen is guilty.What could the news programs have done to reduce the margin of error of the sample percentage of viewers who think that Mr.VanHowen is guilty?

Accepted Answer

The answer of A news program is doing a report...

Question 18

A sample is to be selected from a large population using simple random sampling.The proportion of subjects in the sample that have a given characteristic is to be calculated.Which of the following best describes the sample proportion?
A)It is a parameter.
B)It is a statistic,which is unbiased for the population parameter only if the population is at least 100 times larger than the sample.
C)It is a statistic that is unbiased,and its variability does not depend on the population size provided the population is at least 100 times larger than the sample.
D)It is a lurking variable whose value is unknown.
E)It is a statistic,but its behavior cannot be determined because only one sample is to be taken.

Accepted Answer

The sample proportion is a statistic that is unbiased, and its variability does not depend on the population size provided the population is at least 100 times larger than the sample. This is because simple random sampling ensures that each individual in the population has an equal chance of being chosen, and the sample proportion is calculated based on the number of individuals in the sample with the given characteristic. The larger the sample size, the more accurate the estimate of the population proportion will be, but the variability of the sample proportion will remain constant regardless of population size as long as the sample is small compared to the population.

Question 19

Binomial distributions represent _______ random variables.
A)discrete
B)continuous
C)None of the above

Accepted Answer

Binomial distributions represent the number of successes in a fixed number of trials, which is a discrete random variable. Therefore, the best choice is A) discrete.

Question 20

A researcher is planning to carry out a sample survey in order to estimate the proportion of people in a very large population of interest who have shopped online in the previous 6 months.A simple random sample is to be selected but there is debate about whether to select an SRS of size 500 or of size 1000.With respect to the sample proportion,which statement best describes what can be expected to happen using these two different sample sizes?
A)The statistic will be more biased in the sample of size 500,but the variability of the statistic will be smaller.
B)Using the larger sample size will reduce the bias of the statistic,but the spread of the sampling distribution will be greater.
C)The statistic from either sample size will be unbiased,but the sampling distribution of the statistic from the sample of size 1000 will show greater variability.
D)The statistic from either sample size will be unbiased,but the sampling distribution of the statistic from the sample of size 1000 will show less variability.
E)The sample size has no effect on the sampling distribution of the statistic because the population size is very large.

Accepted Answer

The sample proportion from either sample size will be unbiased because a simple random sample is being used. However, the sampling distribution of the statistic from the sample of size 1000 will show less variability compared to the sample of size 500. This is because as the sample size increases, the variability of the sampling distribution decreases. Therefore, selecting a larger sample size of 1000 would be a better choice to estimate the proportion of people who have shopped online in the previous 6 months in the population of interest.

Quiz 5: Sampling Distributions

The proportion of supermarket customers who do not buy store-brand products is to be estimated.Which of the following scenarios would lead to a sampling distribution of the sample proportion with the lowest variability?

Which histograms display a sampling distribution that is unbiased for estimating the proportion of women at a large university,which is known to be 45%?

Which of the following statements best describes a sampling distribution?

Consider a Poisson distribution with a mean of 4.What is the probability that X < 3?

The figure below shows the Poisson distribution with a mean of 4.The Poisson distribution is an example of _________.

A sample is to be selected from a large population using simple random sampling.The proportion of subjects in the sample that have a given characteristic is to be calculated.Which of the following best describes the sample proportion?

Binomial distributions represent _______ random variables.