Question 1

Recently a group of adults who swim regularly for exercise was evaluated for depression. Each person's depression status was recorded as either currently depressed, likely to get depressed, or not depressed. It turned out that these swimmers were less likely to be depressed than the general population. What sample size was used if the margin of error was about 6%?

Accepted Answer

A sample size of 278 is typically associated with a margin of error around 6% for proportions in a population, assuming a confidence level of 95%.

Question 2

A student organization is trying to decide whether or not to offer more movies on campus. A random sample of students is about to be asked if they are in favor of more free movies on campus. What sample size would be needed to provide a margin of error of about 3%?

Accepted Answer

To achieve a margin of error of about 3% with a 95% confidence level, the sample size needed is approximately 1112, calculated using the formula for margin of error in proportion estimates.

Question 3

During the graduation ceremonies, a student who writes for the school newspaper decides to sample some of the graduating seniors for a quick survey. After the students receive their diploma and step off the stage, he will ask them the question: "Have you already been accepted to college at this point?" What sample size would be needed to provide a margin of error of about 10%?

Accepted Answer

To achieve a margin of error of about 10% in a proportion for a simple random sample, the sample size can be approximated using the formula for the margin of error in a proportion, which is $ME = z \sqrt{\frac{p(1-p)}{n}}$. Without knowing the exact proportion (p) or the z-score (which depends on the confidence level), a rough estimate can be made by assuming p=0.5 (which maximizes the product p(1-p)) and ignoring the z-score for simplicity. Solving for n to get a margin of error of 0.10 (or 10%) with these assumptions leads to needing a sample size around 100. This is a simplification but gives a ballpark figure that is commonly used for such estimations.

Question 4

A random sample of 2000 students showed that 800 were in favor of more movies on campus. Report the results of this poll using the sample proportion and margin of error.

Accepted Answer

The answer of A random sample of 2000 students showed...

Question 5

A random sample of 400 students involved in club activities showed that 250 were women. What is an approximate 95% confidence interval for the proportion of all students involved in club activities who are women?

Accepted Answer

The answer of A random sample of 400 students involved...

Question 6

Two researchers are each conducting a study to estimate a certain population proportion. Researcher A proposes to take a random sample of n = 1000 units from his population of 1 million units. Researcher B proposes to take a random sample of n = 2000 units from his population of 2 million units. For which researcher will the margin of error be the smallest? Explain.

Accepted Answer

The answer of Two researchers are each conducting a study...

Question 7

Use the following information for questions:
 A claim was made that at a local college only 5% of the students that take the introductory statistics course will continue their education in statistics. The Statistics Department at the college believes that this value is too low and decides to conduct a sample survey of 100 students that completed the introductory course the previous term.
-Identify the population.

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 8

Use the following information for questions:
 A claim was made that at a local college only 5% of the students that take the introductory statistics course will continue their education in statistics. The Statistics Department at the college believes that this value is too low and decides to conduct a sample survey of 100 students that completed the introductory course the previous term.
-Of the 100 selected students, 35 reported that they plan to continue an education in statistics. Report the results of this poll using the sample proportion and margin of error.

Accepted Answer

The answer of Use the following information for questions:
 A...

Question 9

Use the following information for questions:
 According to a survey conducted by the Association for Dressings and Sauces (this is an actual association!), 85% of American adults eat salad at least once a week, so that 15% of American adults eat no salad at all! A nutritionist suspects that the percentage (of no-salad eaters) is wrong. She conducts a survey among a sample of adults in her area to test this idea.
-What would be the approximate margin of error if the researcher randomly sampled 2000 adults?

Accepted Answer

The answer of Use the following information for questions:
 According...

Question 10

Use the following information for questions:
 According to a survey conducted by the Association for Dressings and Sauces (this is an actual association!), 85% of American adults eat salad at least once a week, so that 15% of American adults eat no salad at all! A nutritionist suspects that the percentage (of no-salad eaters) is wrong. She conducts a survey among a sample of adults in her area to test this idea.
-What sample size would be needed to provide a margin of error no larger than 2%?

Accepted Answer

The answer of Use the following information for questions:
 According...

Question 11

Which of the following is not true about drawing a simple random sample from a population?

Accepted Answer

A simple random sample does not have a requirement regarding the sample size being no more than 5% of the population size. This principle ensures that every member has an equal chance of selection, but there's no upper limit percentage for the sample size relative to the population.

Question 12

A company has 500 employees and would like to select a simple random sample of 25 of them for a study. Of the following, only one fits the definition of a simple random sample. Which one is it?

Accepted Answer

A simple random sample requires that every member of the population has an equal chance of being selected. Option D achieves this by numbering the employees in random order and then selecting the first 25, ensuring each employee had an equal chance of being included in the sample. Options A, B, and C introduce biases by selecting based on last names, directory pages, or seniority groups, respectively.

Question 13

A class consists of 30 students and the instructor wants to take a simple random sample of 5 students from this class. Which of the following represent the labels that are needed in order to select the sample using a random number table?

Accepted Answer

Since there are 30 students, each student needs a unique label to ensure an equal chance of selection. Using two-digit labels (01, 02, ..., 30) allows for a consistent format that accommodates all 30 students, making it easier to use a random number table.

Question 14

A class consists of 30 students and the instructor wants to take a simple random sample of 5 students from this class. The students are labeled 01 to 30 for the selection process. Which of the following possible samples of size n = 5 is most likely to be selected?

Accepted Answer

In a simple random sample, every subset of a given size has the same chance of being selected. Therefore, all the given options (A, B, and C) are equally likely to be chosen.

Question 15

A population consists of 500 members and a simple random sample of 100 members is to be selected. Which of the following represents the most efficient method for labeling the members for selecting the sample using a random number table?

Accepted Answer

The most efficient method for labeling the members for selecting the sample using a random number table is to assign each member a unique two-digit number. This method ensures that each member has an equal chance of being selected and that the selection process is random.

Question 16

Use the following information for questions:
 The next  question are based on the following row of digits from a random number table. Use these digits to select a random sample following steps 1 through 4 in the text.
00157$\quad$ 37071 $\quad$ 79553 $\quad$ 31062$\quad$ 42411$\quad$ 79371 $\quad$25506$\quad$ 69135
-Suppose that a group of 10 students are numbered from 0 to 9. Draw a simple random sample of 5 students by starting with the digit 1 in the first string of digits 00157. Which 5 students would be selected?

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 17

Use the following information for questions:
 The next  question are based on the following row of digits from a random number table. Use these digits to select a random sample following steps 1 through 4 in the text.
00157$\quad$ 37071 $\quad$ 79553 $\quad$ 31062$\quad$ 42411$\quad$ 79371 $\quad$25506$\quad$ 69135
-Suppose that a group of 50 students are numbered from 01 to 50. Draw a simple random sample of 5 students by starting with the digit 15 from the first string of digits 00157. Which 5 students would be selected?

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 18

Use the following information for questions:
 The next  question are based on the following row of digits from a random number table. Use these digits to select a random sample following steps 1 through 4 in the text.
00157$\quad$ 37071 $\quad$ 79553 $\quad$ 31062$\quad$ 42411$\quad$ 79371 $\quad$25506$\quad$ 69135
-Suppose that a group of 20 students are numbered from 01 to 20. Draw a simple random sample of 5 students by starting with the digit 01 from the first string of digits 00157. Which 5 students would be selected? (Do not use the more efficient method of, for instance, choosing number 1 if 21, 41, 61, or 81 is the random number.)

Accepted Answer

The answer of Use the following information for questions:
 The...

Question 19

Use the following information for questions:
 First Avenue is in desperate need of repaving. The county road commission would like to survey the people who live along this road. They have a list available of all 176 household addresses along First Avenue with the addresses listed in numerical order by address.
-Explain an efficient labeling scheme for taking a simple random sample of 20 household addresses.

Accepted Answer

The answer of Use the following information for questions:
 First...

Question 20

Use the following information for questions:
 First Avenue is in desperate need of repaving. The county road commission would like to survey the people who live along this road. They have a list available of all 176 household addresses along First Avenue with the addresses listed in numerical order by address.
-Using the following stream of random digits, determine the first five selected addresses that would be part of the simple random sample of 20 addresses.
16332 40139 64701 46355 62340 22011 47257 74877

Accepted Answer

The answer of Use the following information for questions:
 First...

Quiz 5: Sampling: Surveys and How to Ask Questions

A student organization is trying to decide whether or not to offer more movies on campus. A random sample of students is about to be asked if they are in favor of more free movies on campus. What sample size would be needed to provide a margin of error of about 3%?

A random sample of 2000 students showed that 800 were in favor of more movies on campus. Report the results of this poll using the sample proportion and margin of error.

A random sample of 400 students involved in club activities showed that 250 were women. What is an approximate 95% confidence interval for the proportion of all students involved in club activities who are women?

Which of the following is not true about drawing a simple random sample from a population?

A company has 500 employees and would like to select a simple random sample of 25 of them for a study. Of the following, only one fits the definition of a simple random sample. Which one is it?

A class consists of 30 students and the instructor wants to take a simple random sample of 5 students from this class. Which of the following represent the labels that are needed in order to select the sample using a random number table?

A class consists of 30 students and the instructor wants to take a simple random sample of 5 students from this class. The students are labeled 01 to 30 for the selection process. Which of the following possible samples of size n = 5 is most likely to be selected?

A population consists of 500 members and a simple random sample of 100 members is to be selected. Which of the following represents the most efficient method for labeling the members for selecting the sample using a random number table?