ST 311 NCSU Exam #1 Multiple Choice

A normal distribution is...

symmetric

In a simple random sample, the problem of non-response bias occurs when...

Some individuals that are randomly selected refuse to participate

A certain firm has 500 employees. An auditor wishes to estimate the average number of days of sick leave taken per employee over the past quarter. The firm has eight divisions, with varying numbers of employees per division. The auditor decides to randomly sample 3 divisions and finds the number of sick days each employee within these divisions take.

This sample is best described as:

A cluster sample using the divisions as clusters.

Suppose a random sample of size n = 35 is taken from population A and a random sample of size n = 20 is taken from population B. In which case would it be valid to use the standard normal distribution to make probability calculations concerning these sample means?

Both samples.

A local corporation was interested in the purchasing habits of Wake County residents. One of the things they were interested in was the proportion of residents that did a major home improvement project in the last year. The corporation used a list of all households in the county to take a simple random sample. The researcher then visited each of the sampled homes and found that 21 of 100 homes had completed a major home improvement project.

A.What is the population of interest in this situation?

B. What is the parameter of interest in this situation?

C. What is the sampling frame in this situation?

A. All Wake County residents.

B. The proportion of all Wake County residents who did a major home improvement. project in the last year.

C. The list of all households in the county

Adult Great Basin rattlesnakes have a mean length of 36 inches and a standard deviation of 5 inches; the length of adult Southern Pacific rattlesnakes is also 36 inches on average, but with a standard deviation of 7 inches. Suppose you take a random sample of 35 Great Basin rattlesnakes and a random sample of 100 Southern Pacific rattlesnakes.

A. Which sample mean is more likely to be larger than 37 inches?

B. You randomly select one Great Basin rattlesnake and one Southern Pacific rattlesnake. Which is more likely be longer than 37 inches? Assume it is known that the length of both subspecies obeys a normal distribution.

A. The sample mean length of the 35 Great Basin rattlesnakes.

B. The Southern Pacific rattlesnake.

. An environmental research firm wants to estimate the proportion of cars in Jackson County, Missouri that would be considered SUVs. Using the county's vehicle registration records they randomly select 220 vehicles. From that list they determined that 90 of them were SUVs. The sample proportion is 0.409, and the 95% confidence interval for the proportion of cars in Jackson County that are SUVs is (0.344, 0.474).

Which of the following would produce a larger margin of error?

If we used 99% confidence instead of 95%

A teacher decided to bring a jar of 530 pieces of small candy to his 33-student classroom so students could practice estimation. The students were told that whoever had the closest guess would win the candy. The average number of pieces of candy guessed by the students was 400, with a standard deviation of 300.

A histogram of the number of pieces of candy the students guessed is most likely to be:

skewed

A college professor has two large lectures (morning and afternoon) each with 250 students. She recorded the scores for her midterm exam from both sections. The resulting scores are presented in these boxplots.

A) From the boxplot we can see that the shape of the histogram of the afternoon section scores has which of the following features:

A. It is right skewed.

B. It is bimodal.

C. It will have several outliers.

D. None of the above.

B) What is the interquartile range for the morning section scores?

A. 20.

B. 68 to 72.

C. 60 to 80.

D. 4.

A)

D. none of the above

B)

D. 4

. The term sampling variability refers to:

The spread in sample statistics that results from selecting different random samples.

A graduate student is interested in estimating the percentage of North Carolina State University students that have an Amazon Prime account. The graduate student believes that this percentage is related to the age of the students.

A) In this situation, what is the population of interest?

B) In this situation, what is the parameter of interest?

A) All students at North Carolina State University.

B) The proportion of all students at North Carolina State University that have an Amazon Prime account.

We would like to construct a 66% confidence interval for the proportion of voters that support building a new prison. What is the appropriate multiplier (z) that would be used in this situation?

0.95

A large company is interested in knowing what proportion of their employees are paid sales commissions as part of their compensation; last year, a census indicated that 7% received sales commissions. The director of human resources is going to take a random sample of 150 employees to complete a survey about compensation, and finds that 12% of employees sampled received sales commissions.

Which is the margin of error for a 95% confidence interval for the true proportion of all employees that received sales commissions?

0.0520

A local politician is interested in the public opinion regarding a tax increase to fund improvements to the local public transportation services in Wake County. She decided to take a random sample of 15 voting precincts and polls all the registered voters within those precincts. (Assume that every voter in each of the 15 precincts responds to the poll.)

This is an example of a:

Cluster random sample.

Which of the following is not a characteristic of the standard normal distribution?

A. It is centered at 0.

B. The standard deviation is 1.

C. It is symmetric.

D. It is skewed to the right.

D. It is skewed to the right.

A biased sample is undesirable since some individuals of the targeted population will be more likely to be sampled than others. Which of the following is an example of a biased sampling scheme?

Convenience sample

We are interested in knowing more about the number of hours students study for ST 311 each week. We know that there are 800 students enrolled in the course, with 35 students per section. We also know that ST 311 students study 10 hours a week on average, and that the standard deviation is 2 hours. We randomly sample 40 students taking the course, and record the average number of hours that they study per week.

A) What is the sample size?

B) What is the standard deviation of the sample mean (also known as the standard error)?

A) 40

B) 0.32

An environmental research firm wants to estimate the proportion of cars in Jackson County Missouri that would be considered SUVs. Using the county's vehicle registration records, they randomly select 220 vehicles. From that list they determined that 90 of them were SUVs. The sample proportion is 0.409, and the 95% confidence interval for the proportion of cars in Jackson County that are SUVs is: (0.344, 0.474).

Which of the following would reduce the margin of error for this confidence interval, assuming the sample proportion did not change?

If we used 90% confidence instead of 95%.

Adult Great Basin rattlesnakes have a mean length of 36 inches and a standard deviation of 5 inches; the length of adult Southern Pacific rattlesnakes is also 36 inches on average, but with a standard deviation of 7 inches. Assume it is known that the length of both subspecies obeys a normal distribution.

Suppose Jafar is a Great Basin rattlesnake and Nagini is a Southern Pacific rattlesnake. Jafar is longer than exactly 75% of all Great Basin rattlesnakes; Nagini is longer than exactly 75% of all Southern Pacific rattlesnakes. Which snake is longer?

Nagini.

Undercoverage occurs when the sampling frame...

does not match the population of interest

Adding 10 to every data point will...

not increase the standard deviation, but will increase the mean

The 'box' in a boxplot...

indicates the start and end of the middle 50% of the data.

The state legislature of Kansas is interested in finding out about the opinion of registered voters throughout the state. The legislative staff has created a plan to randomly select voters from throughout the state. The staff combined the voter registration lists from all the counties in the state to get a single list of all registered voters. Using the list of all voters in the state the staff divided the list into rural and urban voters. The staff then used a random number generator to select 500 rural and 500 urban voters. This sample would best be described as:

A stratified sample of registered voters using rural/urban as strata.

As part of a class project, a college student wanted to estimate the proportion of students at his college that owned a red car. To estimate this proportion he went to a large student parking to during the middle of a class day. He found that 325 out of 10.7 cars (31%) were red. What type of sampling method was used here?

A convenience sample.

Given that a variable X is normally distributed with mean μ and standard deviation σ, why do we convert to a z-score?

Because we can easily find the probabilities from a standard normal

The sampling distribution of a statistic is best described as...

The pattern and frequency with which you observe the statistic

The histogram above gives information about the number of credits taken by a sample of students. Which statement is correct about this histogram?

The histogram is skewed left, so the sample mean is less than the sample median.

. Suppose we want to know the average age of all students taking ST 311 this semester. We take a random sample of 15 students and get a sample mean of 21.4. What is the parameter of interest?

The average of all students taking ST 311 during this semester

Given that a variable X is normally distributed with mean μ and standard deviation σ, why do we convert to a z-score?

Because we can easily find the probabilities from a standard normal

As part of a class project, a college student wanted to estimate the proportion of students at his college that owned a red car. To estimate this proportion he went to a large student parking to during the middle of a class day. He found that 325 out of 10.7 cars (31%) were red. What type of sampling method was used here?

A convenience sample.

voluntary response sample definition

A sample which involves only those who want to participate in the sampling

convenience sample definition

consists of members of a population that are easily accessed (bias because it was easy)

stratified random sampling definition

separation of the target population into different groups, called strata, and the selection of samples from each stratum

*more focused on hitting every group*

cluster sampling

a sampling technique in which clusters of participants that represent the population are used. No reason to believe groups are different; sampling every person in those groups.

undercoverage definition

sample frame is not hitting entire population

ex) only looking at GPA of ST 311 students and not the GPA's of all NC State students

nonresponse bias definition

no one responds

response bias

answers survey but lies

z score formula

z=(x-mean)/standard deviation aka. y-mean/sigma

sampling variablility defintion

variation in sample statisics that results from selecting different random samples

-predictable

sampling distribution of a proportion

1) random sample

2) np greater than or equal to 10

3) nq greater than or equal to 10

4) sigma p-hat = the square root of p timess q divided by n

5) q= 1-p

sampling distribution of the mean

1) random sample

2) n is greater than or equal to 30

sigma y-bar = sigma divided by the square root of n