Question 1

Use the following information for questions:
 For each study, decide if the two samples are :
-A study compared the average number of courses taken by a random sample of 100 freshmen at a university with the average number of courses taken by a separate random sample of 50 freshmen at a community college.
A) Independent samples
B) Paired samples

Accepted Answer

The two samples are from different groups (university freshmen vs. community college freshmen) and are selected randomly without any pairing or matching, making them independent samples.

Question 2

Use the following information for questions:
 For each study, decide if the two samples are :
-A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students). The groups were followed for 2 weeks and the proportions of students with colds were compared.
A) Independent samples
B) Paired samples

Accepted Answer

The two groups (vitamin C and placebo) are separate and do not have any pairing or matching between their members, making them independent samples.

Question 3

Use the following information for questions:
 For each study, decide if the two samples are :
-A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.
A) Independent samples
B) Paired samples

Accepted Answer

The two samples are considered paired because they consist of the same group of students measured at two different times (before and after watching the movie), making the measurements inherently linked or paired.

Question 4

Use the following information for questions:
 For each study, decide if the two samples are :
-In a random sample of 100 students (60 women and 40 men), the average hours of sleep during finals week were compared.
A) Independent samples
B) Paired samples

Accepted Answer

The two samples (women and men) are independent of each other because the measurement of one sample does not affect the measurement of the other.

Question 5

Use the following information for questions:
 For each study, decide if the two samples are :
-In a random sample of 100 students, the change in hours of sleep for each student during and after finals week were compared.
A) Independent samples
B) Paired samples

Accepted Answer

The two samples are considered paired because they involve the same group of students being measured at two different times (during and after finals week), making their sleep hours naturally paired for comparison.

Question 6

Use the following information for questions:
 For each study, decide if the two samples are :
-A random sample of high school seniors is asked how often (times per week) they eat at a fast-food restaurant. A year later, when the students are freshmen in college, they are asked the same question. The frequencies during the senior year of high school and the freshman year in college are compared.
A) Independent samples
B) Paired samples

Accepted Answer

The samples are considered paired because they involve the same group of individuals measured at two different points in time (during their senior year of high school and then again during their freshman year of college). This means the measurements are inherently linked or paired for each individual.

Question 7

Use the following information for questions:
 For each study, decide if the two samples are :
-In an experiment, students taking French are randomly divided into two groups. Half of the students first take a written exam and a week later an oral exam. The other half of the students take the exams in reverse order. The grades of the oral exam were then compared to the grades of the written exam.
A) Independent samples
B) Paired samples

Accepted Answer

The two samples are paired samples because each student takes both exams, and the performance on one exam is directly compared to the performance on the other exam for the same students.

Question 8

Which one of the following ways of collecting data would not result in paired data?
A) Each person is measured twice.
B) Similar individuals are paired prior to an experiment. Each individual in a pair receives a different treatment.
C) Two different variables are measured for each person.
D) Two independent samples are selected and the same response variable is compared between samples.

Accepted Answer

Paired data involves linked observations, such as measurements on the same subject at different times (A), matched individuals (B), or two variables from the same subject (C). Option D describes independent samples, not paired data, as there's no inherent link between observations in the two groups.

Question 9

Which of the following is an example of paired data?
A) A random sample of students is asked how much money they made during the past summer. Results for males and females are compared.
B) A randomized experiment is done in which volunteers who want to lose weight are randomly assigned to either follow a specified diet or participate in an exercise program for 6 months. At the end of the study the two groups are compared to see which one had a higher proportion of people drop out of the study.
C) An observational study is conducted on a random sample of married couples to compare the average number of hours worked per week for the husband and the wife.
D) A random sample of students is asked on the first day of the quarter how many hours they slept the night before. The question is repeated for a new random sample of students on the first day of finals week.

Accepted Answer

Paired data involves observations that are linked or related in some way, such as measurements taken from the same individual or unit at different times or under different conditions. In choice C, the number of hours worked per week is compared for husbands and wives within the same married couples, making it an example of paired data because the measurements (hours worked) are inherently linked by the marital relationship.

Question 10

Which of the following is an example of a difference in two proportions based on independent samples?
A) A random sample of 1000 voters is asked who they plan to vote for in the upcoming election. The difference is found between the proportion of voters who plan to vote for the Republican candidate and the proportion of voters who plan to vote for the Democratic candidate.
B) Each student in a random sample of 500 sophomores and a random sample of 500 seniors is asked what proportion of classes he or she skips in a typical quarter. The difference in the average responses for the two groups is found.
C) A random sample of 800 adults in the US in 1999 was asked if they support the legalization of marijuana, and another random sample of 800 adults was asked the same question is 2009. The difference in the proportions of adults who supported it in 1999 and 2009 is found.
D) None of the above is an example of a difference in two proportions based on independent samples.

Accepted Answer

The scenario in option C involves comparing the proportions of two independent samples (adults in 1999 and adults in 2009) who support the legalization of marijuana.

Question 11

Use the following information for questions:
 Many undergraduate students are thinking about getting a graduate degree. Do male and female students have equal opinions about this? A survey of undergraduate students at public universities in the state of California revealed the following results: Out of 265 female students, 131 were seriously thinking about applying to graduate school. Out of 233 male students, 130 were seriously thinking about applying to graduate school. We wish to compare the proportions of male and female students who are thinking about getting a graduate degree by calculating a confidence interval for the difference between males and females.
-What is the correct notation for the parameter that is estimated by the confidence interval?
A) $ \mu_1 $ - $ \mu_2 $
B) $ \overline{x_1} $ - $ \overline{x_2} $
C) $ p_1 $ - $ p_2 $
D) $ \hat{p_1} $ - $ \hat{p_2} $

Accepted Answer

The parameter estimated by the confidence interval in this context is the difference between two population proportions, which is correctly denoted as $ p_1 $ - $ p_2 $. This notation is used because the question involves comparing proportions (percentages) of male and female students thinking about graduate school, not means or individual observations.

Question 12

Use the following information for questions:
 Many undergraduate students are thinking about getting a graduate degree. Do male and female students have equal opinions about this? A survey of undergraduate students at public universities in the state of California revealed the following results: Out of 265 female students, 131 were seriously thinking about applying to graduate school. Out of 233 male students, 130 were seriously thinking about applying to graduate school. We wish to compare the proportions of male and female students who are thinking about getting a graduate degree by calculating a confidence interval for the difference between males and females.
-What is the correct notation for the difference $ \frac{130}{233} - \frac{131}{265}$?
A) $ \mu_1 $ - $ \mu_2 $
B) $ \overline{x_1} $ - $ \overline{x_2} $
C) $ p_1 $ - $ p_2 $
D) $ \hat{p_1} $ - $ \hat{p_2} $

Accepted Answer

The notation $ \hat{p_1} $ - $ \hat{p_2} $ represents the difference between sample proportions, which is appropriate for comparing the proportions of male and female students thinking about graduate school.

Question 13

Use the following information for questions:
 A Statistics instructor asked a random sample of female and male students how many hours they exercise each week. Minitab output for a comparison of females and males is shown below. 
-This is an example of data collected using
A) paired data.
B) independent samples.
C) a binomial experiment.
D) matched pairs.

Accepted Answer

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

Question 14

Use the following information for questions: A Statistics instructor asked a random sample of female and male students how many hours they exercise each week. Minitab output for a comparison of females and males is shown below. -What is the correct notation for the parameter that is estimated by the confidence interval given in the output? A) p B) p₁ -p₂ C)$\mu$ D)$ \mu$₁ - $ \mu$₂

Accepted Answer

The confidence interval in the output is estimating the difference between two population means, which is denoted by $ \mu$₁ - $ \mu$₂.

Question 15

Which statement is true about p and $\hat{p}$?
A) They are both parameters.
B) They are both statistics.
C) p is a parameter and $\hat{p}$ is a statistic.
D) $\hat{p}$ is a parameter and p is a statistic.

Accepted Answer

p represents the population proportion, making it a parameter, while $\hat{p}$ represents the sample proportion, making it a statistic.

Question 16

Which statement is true about $ \overline{x} $ and $\hat{p}$ ?
A) They are both parameters.
B) They are both statistics.
C) $ \overline{x} $ is a parameter and $\hat{p}$ is a statistic.
D) $\hat{p}$ is a parameter and $ \overline{x} $ is a statistic.

Accepted Answer

$ \overline{x} $ is the sample mean, and $\hat{p}$ is the sample proportion, both of which are statistics because they are calculated from sample data. Parameters, on the other hand, are values that describe a population.

Question 17

Suppose that a polling organization surveys n = 400 people about whether they think the federal government should give financial aid to the airlines to help them avoid bankruptcy. In the poll, 300 people say that the government should provide aid to the airlines. Which choice gives the correct notation and value for the sample proportion in this survey?
A) $\hat{p}$ = 0.30
B) p = 0.30
C) $\hat{p}$ = 0.75
D) p =0.75

Accepted Answer

$\hat{p}$ = 0.75 is the correct notation and value for the sample proportion, where $\hat{p}$ represents the sample proportion and 300 out of 400 people (which is 0.75 or 75%) say the government should provide aid.

Question 18

Suppose we select a random sample of n = 100 students and find that the proportion of students who said they believe in love at first sight is 0.43. Which statement is not necessarily true?
A) There were 43 students in the sample who said they believe in love at first sight.
B) Based on the information provided by the sample, we cannot determine exactly what proportion of the population would say they believe in love at first sight.
C) $\hat{p}$ = 0.43
D) p = 0.43

Accepted Answer

Statement D is not necessarily true because it assumes the sample proportion ($\hat{p}$ = 0.43) is equal to the population proportion (p), which cannot be determined from a sample without further statistical analysis.

Question 19

Suppose you decide to use the 40 students in your Introduction to Philosophy course as a (convenience) sample. You wish to find out more about students' attitudes toward female priests. You decide to compare the proportion of girls who support the idea of a female priest with the proportion of boys. Define the parameter of interest and give the correct notation.

Accepted Answer

The answer of Suppose you decide to use the 40...

Question 20

Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?
A) Values of a parameter will vary from sample to sample but values of a statistic will not.
B) Values of both a parameter and a statistic may vary from sample to sample.
C) Values of a parameter will vary according to the sampling distribution for that parameter.
D) Values of a statistic will vary according to the sampling distribution for that statistic.

Accepted Answer

Parameters are constants that describe a characteristic of a population, so they do not vary from sample to sample. Statistics, however, are calculated from sample data and can vary from sample to sample, hence they have a sampling distribution.

Quiz 9: Understanding Sampling Distributions: Statistics As Random Variables

Use the following information for questions: For each study, decide if the two samples are : -A group of 100 students were randomly assigned to receive vitamin C (50 students) or a placebo (50 students) . The groups were followed for 2 weeks and the proportions of students with colds were compared.

Use the following information for questions: For each study, decide if the two samples are : -A group of 50 students had their blood pressures measured before and after watching a movie containing violence. The mean blood pressure before the movie was compared with the mean pressure after the movie.

Use the following information for questions: For each study, decide if the two samples are : -In a random sample of 100 students (60 women and 40 men) , the average hours of sleep during finals week were compared.

Use the following information for questions: For each study, decide if the two samples are : -In a random sample of 100 students, the change in hours of sleep for each student during and after finals week were compared.

Which one of the following ways of collecting data would not result in paired data?

Which of the following is an example of paired data?

Which of the following is an example of a difference in two proportions based on independent samples?

Use the following information for questions: A Statistics instructor asked a random sample of female and male students how many hours they exercise each week. Minitab output for a comparison of females and males is shown below. -This is an example of data collected using

Which statement is true about p and $\hat{p}$ ?

Which statement is true about $\overline{x}$ and $\hat{p}$ ?

Suppose we select a random sample of n = 100 students and find that the proportion of students who said they believe in love at first sight is 0.43. Which statement is not necessarily true?

Which of the following statements is correct about a parameter and a statistic associated with repeated random samples of the same size from the same population?