Free Printable Proportion Inference (Unit 5 BVD)

1.

A 90% confidence interval for a population proportion is determined to be 40% to 50%. If the confidence is increased to 95% confidence (while n and p̂ stay the same) the confidence interval will

a)

become wider

b)

become narrower

c)

not change

2.

A 90% confidence interval for a population proportion is determined to be 40% to 50%. If the confidence is decreased to 80% confidence (while n and p̂ stay the same) the confidence interval will

a)

become wider

b)

become narrower

c)

not change

3.

A researcher wishes to estimate the proportion of San Diegans who have visited a Disneyland within the last five years. He wishes to do this with 95% confidence with a margin of error of 0.05 or less. Which Z* should he use?

a)

2

b)

212

c)

1.96

d)

1.645

4.

A researcher wishes to estimate the San Diegans who have visited Disneyland within the last five years. He creates a 95% confidence interval. The interval is (.35, .45). What's the best interpretation of this interval?

a)

He's between 35% and 45% confident his sample proportion of San Diegans = the pop. prop. of San Diegans who have gone to Disneyland in the last 5 years.

b)

He's 95% confident that there's a 35% to 45% chance the null is true.

c)

He's 95% confident that the sample proportion of people who have gone to Disneyland is between 35% and 45%.

d)

He's 95% confident that the population proportion of people who have gone to Disneyland is between 35% and 45%.

5.

A researcher wishes to estimate the San Diegans who have visited Disneyland within the last five years. He creates a 95% confidence interval. The interval is (.35, .45). What was the sample proportion?

a)

10%

b)

5%

c)

40%

d)

Not enough information

6.

A researcher wishes to estimate the San Diegans who have visited Disneyland within the last five years. He creates a 95% confidence interval. The interval is (.35, .45). What was the margin of error?

a)

10%

b)

5%

c)

40%

d)

Not enough information

7.

The 90% interval for a statistics test was given by 72% ± 7%. What is the lower bound for the interval?

a)

7%

b)

72%

c)

65%

d)

79%

8.

Which of the following changes to a study would result in a narrower confidence interval?

a)

increasing the confidence level, increasing the sample size

b)

decreasing the confidence level, decreasing the sample size

c)

increasing the confidence level, decreasing the sample size

d)

decreasing the confidence level, increasing the sample size.

9.

You plan do construct a 92% confidence interval. What critical value (z*) should you use?

a)

-.25

b)

-.40

c)

.04

d)

1.75

10.

You take a poll and find that 34% of the 100 people you asked dislike school lunches. What is the standard error? (HINT: it's juuuuust like the formula for standard deviation but you use p̂ instead of p...)

a)

0.093

b)

0.047

c)

.034

d)

.34

11.

You take a random sample of freshmen and calculate the proportion that have been bullied at some point this year. Of the 290 freshmen, 105 said "yes". Calculate a 90% confidence interval for the true proportion. (HINT: use your calculator).

a)

(36.2%, 46.2%)

b)

(31.85%, 48.15%)

c)

(31.57%, 40.85%)

12.

You take a random sample of freshmen and calculate the proportion that have been bullied at some point this year. You get a confidence interval of (31.57%, 40.85%). The principal says no more than 20% of students get bullied. Do you believe the principal's claim?

a)

Yes, because 20% is in the confidence interval

b)

Yes, because 20% is not in the confidence interval

c)

No, because 20% is in the confidence interval

d)

No, because 20% is not in the confidence interval

13.

You take a random sample of freshmen and calculate the proportion that have been bullied at some point this year. Of the 290 freshmen, 105 said "yes". Last year, the national proportion of freshmen who were bullied was 0.35. Are kids meaner this year? What are the hypotheses for this test?

a)

Ho: p = 0.38 Ha: p = 0.35

b)

Ho: p > 0.35 Ha: p = 0.35

c)

Ho: p = 0.35 Ha: p = 0.38

d)

Ho: p = 0.35 Ha: p > 0.35

14.

Are Fakesville High students meaner than Montgomery High students? To investigate this question you take random samples and look at the proportion of students who have been bullied at each school. What are the correct hypotheses for this test?

a)

Ho: p_f = p_m Ha: p_f ≤ p_m

b)

Ho: p_f≠ p_mHa: p_f = p_m

c)

Ho: p_f= p_mHa: p_f < p_m

d)

Ho: p_f= p_mHa: p_f > p_m

15.

Are Fakesville High students meaner than Montgomery High students? Ho: proportion of bullying is equal. Ha: proportion of bullying at FH is greater than proportion of bullying at MOH.
To investigate this question you take random samples and look at the proportion of students who have been bullied at each school. Your test yields a p-value of 0.0029. Using alpha = 5%, what is your decision?

a)

Reject the Ha, you do have evidence that Fakesville High students are meaner.

b)

Fail to reject the Ho. You don't have evidence that Fakesville High students are meaner.

c)

Reject the Ho. You do have evidence that Fakesville High students are meaner.

d)

Accept the Ho. We have statistically significant evidence that Fakesville High students are not meaner.

16.

Are Fakesville High students meaner than Montgomery High students? Ho: proportion of bullying is equal. Ha: proportion of bullying at FH is greater than proportion of bullying at MOH.
You decide to Reject the Ho. What error might you have possibly made?

a)

Type I

b)

Type II

c)

Power

d)

I'm perfect. What's a mistake?

17.

Are Fakesville High students meaner than Montgomery High students? Ho: proportion of bullying is equal. Ha: proportion of bullying at FH is greater than proportion of bullying at MOH.
What is Type I Error in context?

a)

Saying FH students are meaner but in reality they aren't.

b)

Not saying that FH students are meaner and in reality FH students are meaner.

c)

Saying FH students are meaner and they actually are.

d)

Saying FH students are meaner and in reality MOH students are meaner.

18.

Are Fakesville High students meaner than Montgomery High students? Ho: proportion of bullying is equal. Ha: proportion of bullying at FH is greater than proportion of bullying at MOH.
What is Type II Error in context?

a)

Saying FH students are meaner but in reality they aren't.

b)

Not saying that FH students are meaner and in reality FH students are meaner.

c)

Saying FH students are meaner and they actually are.

d)

Saying FH students are meaner and in reality MOH students are meaner.

19.

Are Fakesville High students meaner than Montgomery High students? Ho: proportion of bullying is equal. Ha: proportion of bullying at FH is greater than proportion of bullying at MOH.
What is Power in context?

a)

Saying FH students are meaner but in reality they aren't.

b)

Not saying that FH students are meaner and in reality FH students are meaner.

c)

Saying FH students are meaner and they actually are.

d)

Saying FH students are meaner and in reality MOH students are meaner.

20.

You perform a test of significance and I calculate a
P-value of 0.06. Which of the following α levels is this value statistically significant at?
I. α = 5%
II. α = 1%
III. α = 10%

a)

III only

b)

I only

c)

I and II

d)

I, II, and III

21.

I have a 92% confidence interval that is (0.22, 0.26). Which of the following could be the 94% confidence interval?

a)

(0.20, 0.24)

b)

(0.20, 0.28)

c)

(0.23, 0.25)

d)

(0.23, 0.27)

22.

I have a 92% confidence interval that is (0.22, 0.26). Which of the following could be the 90% confidence interval?

a)

(0.20, 0.24)

b)

(0.20, 0.28)

c)

(0.23, 0.25)

d)

(0.23, 0.27)

23.

I have a confidence interval that is (0.30, 0.39). What is my sample proportion?

a)

0.30

b)

0.39

c)

1.645

d)

0.345

24.

I have a confidence interval that is (0.30, 0.39). What is my Margin or Error?

a)

0.045

b)

0.09

c)

1.645

d)

Not enough information to determine

25.

Which of the following best sums up the Central Limit Theorem?

a)

When you take larger samples, the variability in the sample distribution will decrease.

b)

When you take larger samples, the variability in the sample distribution will increase.

c)

No matter what the parent population looks like, if you take enough samples and the conditions are met, then the sampling distribution will be the same as the sample distribution.

d)

No matter what the parent population looks like, if you take enough samples and the conditions are met, then the sampling distribution will be approximately Normal

26.

If the M&M company claims that 20% of all M&Ms are blue. Which of the following samples would be the MOST unusual?

a)

Opening a bag with 60 M&Ms and having 15 blue.

b)

Opening a bag with 100 M&Ms and having 25 blue.

c)

Opening a bag with 200 M&Ms and having 50 blue.

d)

Reaching into a bag and the first one you pull out is blue.

27.

A fitness company thinks that the 50% of their members want to use treadmills. But after all the New Year's Resolutions, they're wondering if the proportion has gone up (if it has, then they need to buy more treadmills.) They conduct a hypothesis test and get a p-value of 0.027. This causes them to reject the Null. Which error might they have made?

a)

They say that more people don't want treadmills but they actually do.

b)

They say that more people want treadmills but they actually don't.

c)

They say that less people want treadmills but more people actually do.

d)

They say that more people want treadmills and they actually do.

28.

A fitness company thinks that the 50% of their members want to use treadmills. But after all the New Year's Resolutions, they're wondering if the proportion has gone up (if it has, then they need to buy more treadmills). They conduct a hypothesis test and get a p-value of 0.027. This causes them to reject the Null. What is power in this context?

a)

They say that more people don't want treadmills but they actually do.

b)

They say that more people want treadmills but they actually don't.

c)

They say that less people want treadmills but more people actually do.

d)

They say that more people want treadmills and they actually do.

29.

A fitness company thinks that the 50% of their members want to use treadmills. But after all the New Year's Resolutions, they're wondering if the proportion has gone up (if it has, then they need to buy more treadmills). They conduct a hypothesis test and get a p-value of 0.027. This causes them to reject the Null. What does the p-value mean in context here?

a)

If 50% of members want to use treadmills, then there's a 2.7% chance we'd see a sample that or more unusual.

b)

There's a 2.7% chance that the alternative hypothesis is true.

c)

There's a 2.7% chance that we'd reject the Null and make a Type I error.

d)

There's a 2.7% chance that we'd fail to reject the Null and make a Type II error.

30.

A P-value indicates:

a)

the probability that the null hypothesis is true

b)

the probability that the alternative hypothesis is true

c)

the probability of obtaining the results (or one more extreme) if the null hypothesis is true

d)

probability of a Type I error

31.

Suppose the P-value for a hypothesis test is 0.0304. Using a = 0.05, what is the appropriate conclusion?

a)

a) reject the null

b)

b) reject the alternative

c)

c) Fail to reject the null

d)

d) Fail to reject the alternative

32.

Failing to reject a null hypothesis that is false can be characterized as

a)

a Type I error

b)

a Type II error

c)

both a Type I and Type II error

d)

no error

33.

A Type I error is when:

a)

We obtain the wrong test statistic

b)

We reject the null hypothesis when it is actually true

c)

We fail to reject the null hypothesis when it's actually false

d)

We reject the alternate hypothesis when it's actually true

34.

In testing hypotheses, which of the following would be strong evidence against the null hypothesis?

a)

using a small level of significance

b)

using a large level of significance

c)

obtaining data with a small p-value

d)

obtaining data with a low test statistic

35.

A researcher plans to conduct a test of hypotheses at the α = 0.01 significance level. She obtains a z-score of -2.072 and a p-value of 0.038. What is the probability that the researcher commits a Type I error?

a)

0.01

b)

0.10

c)

0.90

d)

0.99

36.

Choose the pair that provide a legitimate hypothesis.

a)

H_o: p≠0.4, H_a: p>0.4

b)

H_o:p̂=0.16, H_a: p̂>0.16

c)

H_o:=0.82, H_a:>0.82

d)

H_o:p=0.24, H_a:p<0.24

37.

Which of the following is not a bad thing?

a)

Accepting the Null

b)

Type I Error

c)

Type II Error

d)

Power

38.

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. They'll use this sample to test and see if there's evidence that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the null hypothesis.

a)

H_o: p <.5, where p is the true proportion of Americans who can name one justice currently serving.

b)

H_o:p >.5 where p is the true proportion of Americans who can name one justice currently serving.

c)

H_o:p =.5 where p is the true proportion of Americans who can name one justice currently serving.

39.

In a random sample of 1000 adult Americans, only 430 could name at least one justice who is currently serving on the US Supreme Court. They'll use this sample to test the claim is that fewer than half of adult Americans can name at least one justice who is currently serving on the US Supreme Court. State the alternative hypothesis.

a)

H_a: p=.5, where p is the true proportion of Americans who can name one justice currently serving.

b)

H_a: p>.5, where p is the true proportion of Americans who can name one justice currently serving.

c)

H_a: p<.5, where p is the true proportion of Americans who can name one justice currently serving.

40.

In a national survey of 2013 adults, 1283 indicated that they believe rudeness is a more serious problem than in years past. Does this indicate that more than 3/4 of American adults believe rudeness is a worsening problem? State the alternative hypothesis.

a)

H_a: p > .75, where p is the true proportion of Americans who believe rudeness is worsening.

b)

H_a: p = .75, where p is the true proportion of Americans who believe rudeness is worsening.

c)

H_a: p <.75, where p is the true proportion of Americans who believe rudeness is worsening.

41.

In a national survey of 2013 adults, 1283 indicated that they believe rudeness is a more serious problem than in years past. Does this indicate that more than 3/4 of American adults believe rudeness is a worsening problem? State the null hypothesis.

a)

H_o: p > .75, where p is the true proportion of Americans who believe rudeness is worsening.

b)

H_o: p = .75, where p is the true proportion of Americans who believe rudeness is worsening.

c)

H_o: p < .75, where p is the true proportion of Americans who believe rudeness is worsening.

42.

The Associated Press found that 730 of 1000 randomly selected adults preferred to watch movies at home rather than at a movie theater. Is there convincing evidence that the majority of adult Americans prefer watching movies at home? State the alternative hypothesis.

a)

H_a: p = .50, where p is the true proportion of adult Americans who prefer watching movies at home.

b)

H_a: p < .50, where p is the true proportion of adult Americans who prefer watching movies at home.

c)

H_a: p > .50, where p is the true proportion of adult Americans who prefer watching movies at home.

43.

The Associated Press found that 730 of 1000 randomly selected adults preferred to watch movies at home rather than at a movie theater. Is there convincing evidence that the majority of adult Americans prefer watching movies at home? State the null hypothesis.

a)

H_o: p = .50, where p is the true proportion of adult Americans who prefer watching movies at home.

b)

H_o: p > .50, where p is the true proportion of adult Americans who prefer watching movies at home.

c)

H_o: p < .50, where p is the true proportion of adult Americans who prefer watching movies at home.

44.

In a survey of 526 US businesses, 400 indicated that they monitor employee's web site visits. Is there sufficient evidence that more than 70% of US businesses monitor employees' web site visits? State the null hypothesis.

a)

H_o: p = .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

b)

H_o: p < .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

c)

H_o: p > .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

45.

In a survey of 526 US businesses, 400 indicated that they monitor employee's web site visits. Is there sufficient evidence that more than 70% of US businesses monitor employees' web site visits? State the alternative hypothesis.

a)

H_a: p = .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

b)

H_a: p > .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

c)

H_a: p < .70, where p is the true proportion of US businesses that indicated they monitor employee web sites.

46.

z-scores closer to 0 indicate...

a)

Stronger evidence against the null.

b)

Weaker evidence against the null.

Proportion Inference (Unit 5 BVD)

Total questions: 46

Worksheet time: 3hrs 32mins

Similar Resources on Wayground