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##### Stats Final Exam

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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

Which of the the following techniques is best used for QUANTITATIVE data?

A) Histogram

B) Pie Chart

C) Two-way Table

D) Bar Chart

4. Find the mean for the following set of values: 12, 14, 19, 13, 17.

A) 14.5

B) 14

C) 18.75

D) 15

5. 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.

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

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.

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

The y-intercept of a regression equation is interpreted as:

A) The predicted value of y when x equals 0.

B) The change in y for a one unit change in x.

C) The amount of variation in y explained by x.

Which of the following correlations would have the weakest linear relationship?

A) r = 0.9

B) r = -0.7

C) r = -0.1

D) r = 0.6

In general, which is more likely to contain the unknown population mean?

A) A 90% confidence interval

B) A 95% confidence interval

C) A 99% confidence interval

D) They are all equally likely

Suppose a 95% confidence interval for the proportion of Americans who smoke is 0.178 to 0.242. Which one of the following statements is NOT true?

A) It is reasonable to say that more than 25% of Americans smoke.

B) It is reasonable to say that less than 25% of Americans smoke.

C) It is reasonable to say that more than 17% of Americans smoke.

D) An \\\"acceptable\\\" hypothesis is that about 19% of Americans smoke.

Suppose there is a project to study the effectiveness of a new treatment for high cholesterol. To test whether the new treatment lowers cholesterol level, cholesterol readings were recorded on same participant before and after a 10-week treatment period. What kind of test would you recommend for this study?

A) a two sample t-test

B) a paried t-test

C) a two proportion test

D) an unpooled t-test

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

We test if the average number of hours studied for college freshman is different from the average number of hours studied for seniors in college.

A) Paired

B) Independent

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

Rent charged (in dollars) and apartment size (in sq. ft.) of a sample of one-bedroom apartments in State College.

A) Bar Graph

B) Histogram

C) Two-way table

D) Scatterplot

E) Side-by-Side Boxplots

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

Whether a person is a vegetarian and Gender.

A) Bar Graph

B) Histogram

C) Two-way table

D) Scatterplot

E) Side-by-Side Boxplots

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

Predictor Coef Se COEF T P

Constant -21.04 16.00 -.1.32 0.205

X1 0.566 0.1475 3.84 0.001

Using the above regression output, what would be the predicted value of y for x = 20?

A) -21.04

B) 0.5666

C) 32.37

D) -9.71

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

We test the IQ of a random sample of children of women smokers to see if their mean IQ is lower than the national mean IQ of 100.

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

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

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

29. 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

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

We test if the average age of marriage for women in the United States is different from 27.

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

We test if the average number of hours studied for college freshman is different from the average number of hours studied for seniors in college.

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

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

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

A researcher wants to compare the testosterone levels among athletes in four sports: soccer, track, Lacrosse, and water polo. A sample is drawn in the following manner with total sample size was n =30 (10 soccer, 10 track, 5 Lacrosse, and 5 water polo).

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

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:?1 - ?2 = 0

D) H0:x-bar1 - x-bar2 = 0

Select the proper NULL hypothesis:

A class survey is used to compare the beliefs in love at first sight for males and females.

A) H0:p1 - p2 = 0

B) H0:p-hat1 - p-hat2 = 0

C) H0:µ1 - µ2 = 0

D) H0:x-bar1 - x-bar2 = 0

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

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

Students are asked whether they have ever missed class as a result of drinking alcohol. Results for fraternity and sorority members are compared to results for non-Greeks.

A) Independent

B) Paired

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.

Accepted

Yes No Total

Female 45 35 80

Male 85 35 120

Total 130 70 200

What are the odds of acceptance for females?

A) 45/35

B) 45/80

C) 35/80

D) 45/200

Test of p=0.2 vs p not=0.2

Event=yes

Variable X N Sample P 95% CI Z-value p-Value

Smoke 5 35 0.142857 (0.026928,0.258786) -0.85 0.398

Based on the output above, what statistical conclusion should you reach? The percentage of STAT 200 students who smoke:

A) does not differ from 20%

B) is less than 20%

C) is different than 20%

D) is greater than 14%

14.Test of p=0.2 vs p not=0.2

Event=yes

Variable X N Sample P 95% CI Z-value p-Value

Smoke 5 35 0.142857 (0.026928,0.258786) -0.85 0.398

Based on the output above, what is the value of the sample statistic?

A) 0.2

B) 0.142

C) -0.85

D) 0.398

Test of mu=3.5 vs<3.5

Variable N Mean STDEV T

GPA 25 3.15 0.50 -3.00

Based on the above output what is the standard error of the mean?

A) 0.10

B) 0.50

C) 12.5

Test of mu=3.5 vs<3.5

Variable N Mean STDEV T

GPA 25 3.15 0.50 -3.00

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

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

A class survey is used to compare the GPAs of male and female students.

A) Independent

B) Paired

There are five children in your family (you and 4 siblings). Each night, two children are responsible to wash the dishes. To be fair, the children are selected by randomly pulling names from a hat. What is the probability that you will not have to wash the dishes?

A) 4/25

B) 12/20

C) 4/20

D) 12/25

Suppose you are taking a statistics course and a psychology course next semester. You like mathematics, so you believe that probability of getting an \\\"A\\\" in statistics is 0.8. On the other hand, psychology is not as interesting to you so the probability of getting an \\\"A\\\" in that class is 0.6. It will be challenging to manage both courses at the same time, so the probability of getting an \\\"A\\\" in both classes is 0.5. Are the events \\\"A\\\" in statistics and \\\"A\\\" in psychology independent?

A) No because 0.8*0.6 does not equal 0.5.

B) Yes because the grade in statistics does not affect the grade earned in psychology.

C) Yes because 0.8*0.6 does not equal 0.5.

A researcher randomly selected 20 classes of Grade-1 students from all elemetary schools in New York State to form a sample of students to study relationship bewteen nutrition and school performance. This sampling method is BEST defined as:

A) Simple random sampling

B) Cluster sampling

C) Stratified random sampling

D) Convenience sampling

Which of the following best describes the standardized (z) score for an observation?

A) It is the number of standard deviations the observation falls from the mean.

B) It is the most common score for that type of observation.

C) It is one standard deviation more than the observation.

D) It is the center of the list of scores from which the observation was taken.

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

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

According to a recent survey approximately 25% of all college students work full time (that is, there is 0.25 probability for any given student to work full time). If the random variable X represents the number of students who work full time in samples of size 10, what is the expected value of X?

A) 2.0

B) 2.5

C) 3.0

Which of the following is the main advantage of randomized experiments, when compared to observational studies?

A) The participants are more likely to stick with the experiment for the full duration

B) Cause and effect conclusions are possible.

C) Random assignment ensures that the two sample sizes are equal and that requirement is necessary.

D) Random assignment guarantees a more representative sample.

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.

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.

Sample X N Sample P

1 25 90 0.277778

2 30 90 0.333333

Difference =p(1)-p (2)

Estimate for difference -0.0555556

95% CI for difference: (-0.189898, 0.0787873)

Test for difference =0 (vs not=0): z=-0.81 p-value=0.418

From the output above comparing proportions between Group A and Group B, what decision can be made?

A) With a p-value of 0.418 we can reject the null hypothesis and conclude that the proportions who would buy the product differ for Group A and Group B.

B) With a p-value of 0.418 we cannot reject the null hypothesis and conclude that the proportions who would buy the product do not differ for Group A and Group B.

C) With a p-value of 0.418 we can reject the alternative hypothesis and conclude that the proportions who would buy the product differ for Group A and Group B.

D) With a p-value of 0.418 we cannot reject the alternative hypothesis and conclude that the proportions who would buy the product differ for Group A and Group B.

Source DF SS MS F P

GRADE 3 1.79.7264 59.9088 678.13 0.000

ERROR 301 26.5916 0.0883

TOTAL 304 206.3180

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

Which of the following IS a part of the 5-number summary?

A) Maximum

B) IQR

C) Range

D) Standard deviation

E) All of choices are not part of the 5-number summary.

According to a recent survey approximately 25% of all college students work full time (that is, there is 0.25 probability for any given student to work full time). If the random variable X represents the number of students who work full time in samples of size 10, what is the standard deviation of X?

A) 2.5

B) 1.875

C) 1.37