# Statistics 50 multiple choice questions

1.
Which of the following is a matched pairs design?
A) Measure levels of depression for a random sample of internet users and for a random sample of non-users.
B) Measure level of depression for a random sample on non-internet users: provide them with internet use for a year and then measure their level of depression.

2.
Which of the the following techniques is best used for QUANTITATIVE data?
A) Histogram
B) Pie Chart
C) Two-way Table
D) Bar Chart

3.
Suppose the distirbution of speeds at an interstate highway location is bell-shaped with a mean of 73mph and a standard deviation of 4mph. About 95% of vehicles at this location travel between ____ and ____ mph?
A) 65 and 81 mph
B) 69 and 77 mph
C) 61 and 85 mph

4.
Which one of the following variables is discrete?
A) The number of automobiles produced by Ford
B) The daily high temperature in Chicago
C) The age of the students in our class
D) The weight of the students in our class
E) The manufacturer of an automobile

5.

From the histogram above, which of the following would we expect to be true?
A) The median would be less than the mean
B) The median would be greater than the mean
C) The median would be equal with the mean

6.
Find the mean for the following set of values: 12, 14, 19, 13, 17.
A) 14.5
B) 14
C) 18.75
D) 15

7.
A study found that students who procrastinate are more likely to get colds. A sample of 300 college students was asked how often they procrastinate and if they’ve had a cold in the last two months. Below is a two-way table of counts (rows = whether or not procrastinates).

State the appropriate null hypotheses for this study.
A) There is no relationship in the population between Procrastination and Having a Cold.
B) There is no relationship in the sample between Procrastination and Having a Cold.
C) There is relationship in the population between Procrastination and Having a Cold.
D) There is relationship in the sample between Procrastination and Having a Cold.

8.
A research project was conducted to study whether gender plays a role in the acceptance of a student into vocational education programs. A random sample of 200 applicants for vocational education was selected from a school district. The data were then summarized into table shown below.

The appropriate alternative hypotheses for this study is that gender and acceptance are associated.
A) True
B) False

9.
A research project was conducted to study whether gender plays a role in the acceptance of a student into vocational education programs. A random sample of 200 applicants for vocaional education was selected from a school district. The data were then summarized into table shown below.

What are the odds of acceptance for females?
A) 45/35
B) 45/80
C) 35/80
D) 45/200

10.

Using the above regression output, what is the correct regression equation?
A) y-hat = – 21.04 + 0.5666X1
B) y-hat = 0.5666 – 21.04X1
C) y-hat = 16.00 + 0.1475X1
D) y-hat = 16.00 + 0.5666X1

11.

Using the above regression output, then the correlation between X1 and Y would be calculated by taking:
A) The positive square root of 0.45
B) 0.45 times 0.45
C) The negative square root of 0.45

12

Using the above regression output, how much of the variation in Y is explained by X1?
A) 45%
B) 42%
C) The positive square root of 0.45
D) 3.98537%

13.

Based on the output above, what are the null and alternative hypotheses?
A)   Ho: p = 0.2   Ha: p ≠ 0.2
B)   Ho: p−hat = 0.2   Ha: p−hat ≠ 0.2
C)   Ho: p = 0.2   Ha: p < 0.2
D)   Ho: p−hat = 0.2   Ha: p−hat < 0.2
E)   Ho: μ = 0.2   Ha: μ < 0.2
F)   Ho: μ = 0.2   Ha: μ ≠ 0.2

14.

Based on the output above, what is the value of the test statistic?
A) 0.2
B) 0.142
C) -0.85
D) 0.398

15.

Based on the above output what is the standard error of the mean?
A) 0.10
B) 0.50
C) 12.5

16.

Based on the output above, what would be the degrees of freedom used to find the p-value?
A) 25
B) 24
C) 3.5
D) 3.15

17.
From a class survey, 90% confidence intervals were created for both the females and males who responded Yes to having smoked marijuana. The 90% confidence intervals were 0.417 to 0.565 for the females and 0.437 to 0.609 for the males. What conclusions can we draw in regards to the population proportions of females and males who said that they have tried marijuana?
A) We cannot conclude there is a difference between the population proportions.
B) We cannot conclude there is a difference between the sample proportions.
C) Males are more likely than females to have tried marijuana.
D) Males are less likely than females to have tried marijuana.

18.
Which of the following quantities does NOT affect sample size for estimating a population mean?
A) the confidence level
B) the sample standard deviation
C) the margin of error
D) the sample mean

19.
If you were conducting a two sample T−test to compare two means, which of the following would allow you to properly use the pooled method in order to perform the test?
A) If the larger sample standard deviation was 5 and the smaller sample standard deviation was 4
B) If the larger sample mean was 5 and the smaller sample mean was 4
C) If the larger standard error was 5 and the smaller standard error was 4

20.
Two TV commercials are developed for marketing a new product. 180 people have been randomly selected and split into two groups of 90 each. In a controlled setting, Group A watches commercial A and Group B watches commercial B. In Group A, 25 say they would buy the product. In Group B, 30 say they would buy the product.

To test which commercial has better effect, two proportion z test could be applied here since all assumptions have been satisfied.
A) True
B) False

21.
Identify whether the comparison is based on two independent samples or paired data:

We test if the average number of hours studied by all college freshman living in a particular dorm for their math course differs from number of hours studied in their chemistry course during a particular semester for each student in the study.
A) Paired
B) Independent

22.

Based on the above ANOVA output, how many means are being tested?
A) 4
B) 3
C) 301
D) 304

23.

Based on the above ANOVA output, what conclusion should be made regarding the means?
A) With p-value of 0.000 conclude that not all of the means are equal.
B) With p-value of 0.000 conclude that all of the means are different
C) With p-value of 0.000 conclude that all of the means are equal

24.
Based on the number and types of variables present, select the most appropriate display for each of the following:

Number of Hours spent watching TV per day for a representative sample of Americans.
A) Bar Graph
B) Histogram
C) Two-way table
D) Scatterplot
E) Side-by-Side Boxplots

25.
Based on the number and types of variables present, select the most appropriate display for each of the following:

Actual Height (in inches) and Ideal Height (in inches) for a representative sample of PSU students.
A) Bar Graph
B) Histogram
C) Two-way table
D) Scatterplot
E) Side-by-Side Boxplots

26.
Select the most appropriate statistical test for each of the following:

We examine a random sample of State College apartments to see on average how much rent increases per unit increase of square footage:
A) 1 Proportion Test
B) 1 mean test with a one-sided alternative
C) 1 mean test with a two-sided alternative
D) Two-sample t-test with a one-sided alternative
E) Two-sample t-test with a two-sided alternative
F) Chi-square test
G) One-Way ANOVA test
H) Regression

27.
Select the most appropriate statistical test for each of the following:

We take random samples of African-American, White, Asian, and Hispanic workers to determine if mean earnings differ among these groups:
A) 1 Proportion Test
B) 1 mean test with a one-sided alternative
C) 1 mean test with a two-sided alternative
D) Two-sample t-test with a one-sided alternative
E) Two-sample t-test with a two-sided alternative
F) Chi-square test
G) One-Way ANOVA test
H) Regression

28.
Select the most appropriate statistical test for each of the following:

We want to test for a relationship between race and employment status (employed or unemployed):
A) 1 Proportion Test
B) 1 mean test with a one-sided alternative
C) 1 mean test with a two-sided alternative
D) Two-sample t-test with a one-sided alternative
E) Two-sample t-test with a two-sided alternative
F) Chi-square test
G) One-Way ANOVA test
H) Regression

29.
Select the most appropriate statistical test for each of the following:

We want to test if men have a higher salary than women in the field of engineering using a random sample of male engineers and a random sample of female engineers.
A) 1 Proportion Test
B) 1 mean test with a one-sided alternative
C) 1 mean test with a two-sided alternative
D) Two-sample t-test with a one-sided alternative.
E) Two-sample t-test with a two-sided alternative.
F) Chi-square test
G) One-Way ANOVA test
H) Regression

30.
Select the most appropriate statistical test for each of the following:

We want to test if more than 50% of children get a cold each Winter.
A) 1 Proportion Test
B) 1 mean test with a one-sided alternative
C) 1 mean test with a two-sided alternative
D) Two-sample t-test with a one-sided alternative
E) Two-sample t-test with a two-sided alternative
F) Chi-square test
G) One-Way ANOVA test
H) Regression

31.
Select the most appropriate statistical test for each of the following:

A researcher wants to see if female Caucasians are more likely to have blue eyes than male Caucasians. What hypothesis test should be used?
A) One population proportion
B) Difference between two population proportions
C) One population mean
D) Population mean difference (paired data)
E) Difference between two population means (independent data)

32.
Select the most appropriate statistical test for each of the following:

We survey a random sample of households in Philadelphia to test if less than 50% of families are families where both parents are working full time.
A) T-test about a mean with a one-sided alternative
B) T-test about a mean with a two-sided alternative
C) Chi-square test of independence
D) Z-test about a proportion with a one-sided alternative
E) Z-test about a proportion with a two-sided alternative
F) One-way Analysis of Variance (ANOVA)
G) Regression

33.
Select the most appropriate statistical test for each of the following:

We test if the mean rent of all downtown Pittsburgh one bedroom apartments is different from the mean rent of all non-downtown one bedroom apartments by examining a random sample of downtown one-bedroom apartments and a random sample of non-downtown one-bedroom apartments.
A) 1 Proportion Test
B) 1 mean test with a one-sided alternative
C) 1 mean test with a two-sided alternative
D) Two-sample t-test with a one-sided alternative
E) Two-sample t-test with a two-sided alternative
F) Chi-square test
G) One-Way ANOVA test
H) Regression

34.
Select the proper NULL hypothesis:

Fifty students have their blood pressures before and after an exam. We wish to know if there is an increase, on average.
A) H0:pd = 0
B) H0:p-hat1 – p-hat2 = 0
C) H0:μd = 0
D) H0:x-bar1 – x-bar2 = 0

35.
Select the proper NULL hypothesis:

A class survey is used to compare the GPAs of male and female students.
A) H0:p1 – p2 = 0
B) H0:p-hat1 – p-hat2 = 0
C) H0:μ1 – μ2 = 0
D) H0:x-bar1 – x-bar2 = 0

36.
Select the proper NULL hypothesis:

A study was conducted to see if there is a difference between blood pressures of husbands and their wives.
A) H0:pd = 0
B) H0:p-hat1 – p-hat2 = 0
C) H0:µd = 0
D) H0:x-bar1 – x-bar2 = 0

37.
Identify whether the comparison is based on two independent samples or paired data:

In a nationwide survey, people are asked if they think crime is a problem in their town or not. The proportion saying yes is compared for people from large cities versus people in small towns and rural areas.
A) Independent
B) Paired

38.
Identify whether the comparison is based on two independent samples or paired data:

Fifty students have their blood pressures before and after an exam. We wish to know if there is an increase, on average.
A) Independent
B) Paired

39.
A statistics class has 4 teaching assistants (TAs): three female assistants (Lauren, Rona, and Leila) and one male assistant (Josh). Each TA teaches one discussion section. A student picks a discussion section. The two events W = {the TA is a woman} and J = {the TA is Josh} are
A) independent events.
B) mutually exclusive events.
C) each simple events.
D) None of the above.

40.
Three people are selected randomly one at a time from a group of 10 people as representatives of the group. The group consists of 3 female and 7 male. What is the probability for the three people selected to consist of (by order of selection): Female, Female, Male.
A) 0.809524
B) 0.97619
C) 0.015873
D) 0.0583

41.
Which one of the following statements is true?
A) Increasing the sample size of a survey decreases the margin of error.
B) Increasing the sample size of a survey increases the margin of error.
C) Increasing the sample size of a survey decreases the impact of response bias.
D) Increasing the sample size of a survey increases the impact of response bias.

42.
In order to test if a coin is a fair coin, the coin is tossed 100 times and the results (Head or Tail) were recorded for analysis. What is the sample in this study?
A) the coin
B) the outcomes of the 100 tosses
C) probability of the coin to show Head
D) percentage of Heads in the 100 outcomes

43.
Which of the following is NOT part of the 5-number summary?
A) Mean
B) Median
C) Maximum
D) Minimum
E) All of choices are part of the 5-number summary.

44.
Exams scores (in percentages) range from 0 to 100. Suppose an exam for STAT 200 was easy and most of the students scored very well with only a few students scoring low. Which would best describe the shape of the distribution?
A) Right skewed
B) Left skewed
C) Bell-shaped
D) Not enough information to tell

45.
A student does not study for a 10 question multiple choice quiz, with five answer choices for each question, so he randomly guesses an answer for every question. Which choice below describes how to find the probability that this student gets exactly 7 questions correct?
A) Find cumulative probability for 7 successes for a binomial variable with n = 10 and p = 7/10.
B) Find cumulative probability for 7 successes for a binomial variable with n = 10 and p = 1/5.
C) Find probability of 7 successes for a binomial variable with n = 10 and p = 1/5
D) Find probability of 7 successes for a binomial variable with n = 10 and p = 7/10

46.
Correctly identify whether the following situations satisfy the conditions required to conduct a Binomial experiment. Rolling a die many times and observing whether the number obtained is even or odd
A) Binomial
B) NOT Binomial

47.
Suppose that for X = net amount won or lost in a lottery game, the expected value is E(X) = -\$0.50. What is the correct interpretation of this value?
A) The most likely outcome of a single play is a net loss of 50 cents.
B) A player will have a net loss of 50 cents every single time he or she plays this lottery game.
C) Over a large number of plays the average outcome for plays is a net loss of 50 cents.
D) A mistake must have been made because it’s impossible for an expected value to be negative

48.
Suppose that X=number of heads out of 12 independent flips of a fair coin. What is the expected value of x?
A) 6
B) 12
C) 5
D) 3

49.
The purpose of having a control group in a study is
A) to estimate the response when the treatment is not applied.
B) to decrease the margin of error.
C) to be able to blind the subjects.
D) to make the samples more representative.

50.
Randomly chosen 988 American adults participated in a poll regarding whether to approve a new gun control legislation. What is the parmaeter of interest in this study?
A) the proportion of American adults who approve the new gun control legislation
B) the proportion of the 988 people who approve the the new gun control legislation
C) Is the new gun control legislation beneficial to society
D) the number of people in poll who were against the new gun control legislation

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