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Hypothesis Testing 1

Total questions: 45

Worksheet time: 1hrs 9mins

Name

Class

Date

Which of the following represents the appropriate null & alternative hypotheses?

The mean height of women is greater than 64"

H₀: μ > 64"

Hₐ: μ ≠ 64"

H₀: μ < 64"

Hₐ: μ > 64"

H₀: p > 64"

Hₐ: p ≠ 64"

H₀: p = 64"

Hₐ: p > 64"

Identify the correct null hypothesis:

Is the proportion of babies born male different from 50%? In a sample of 200 babies, 96 were male. Test the claim using a level of significance of 1%.

H₀: p = 0.50

H₀: µ = 100

H₀: p = 0.48

H₀: µ = 96

When performing a test about the population proportion, what distribution would you need to use?

chi-square

Which of the following shows a right-tailed test?

Ha: µ < 15

H₀: µ < 15

Ha: µ > 15

H₀: µ > 15

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

using a small level of significance

using a large level of significance

obtaining data with a small p-value

obtaining data with a low test statistic

What is the critical value (in a test about proportions) for a left-tailed test with α = 0.05 and n ≥ 30.

z₀ = -1.645

z₀ = -2.33

z₀ = -1.96

z₀ = 2.58

A P-value indicates:

the probability that the null hypothesis is true

the probability that the alternative hypothesis is true

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

probability of a Type I error

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

a) Reject the null hypothesis

b) Reject the alternative hypothesis

c) Fail to reject the null hypothesis

d) Fail to reject the alternative hypothesis

When p-value is greater than alpha we:

Reject Ho

Fail to reject Ha

Fail to reject Ho

Reject Ha

10.

A mayor is concerned about the percentage of city residents who express disapproval of his job performance. His political committee pays for a newspaper ad, hoping to keep his disapproval rating below 21%. They will use a follow up poll to access effectiveness. What are the correct null and alternative hypotheses?

Ho: μ > 21

Ha: μ < 21

Ho: p > .20

Ha: p < .20

Ho: p < .21

Ha: p > .21

Ho: p > .21

Ha: p < .21

11.

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

12.

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

13.

A one sample t-test is conducted on Ho : μ = 81.6. The

sample has a sample mean = 84.1 , s = 3.1, n = 25, and α = .01.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

14.

A one sample t-test is conducted on Ho : μ = 81.6. The

sample has a sample mean = 84.1 , s = 3.1, n = 25, and α =

.01.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

15.

In performing a hypothesis test where the null

hypothesis is that the μ = 6.9. A random sample of 16

items is selected. The sample mean is 7.1 and the sample

standard deviation is 2.4. It can be assumed that the

population is normally distributed at α = .05.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

16.

In performing a hypothesis test where the null

hypothesis is that the μ = 6.9. A random sample of 16

items is selected. The sample mean is 7.1 and the sample

standard deviation is 2.4. It can be assumed that the

population is normally distributed at α = .05.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

17.

A fast food outlet claims that the mean waiting time in

line is less than 1.9 minutes. A random sample of 20

customers has a mean of 1.7 minutes with a standard

deviation of 0.8 minute. If α = 0.05, test the fast food

outlet's claim using P-values.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

18.

A fast food outlet claims that the mean waiting time in

line is less than 1.9 minutes. A random sample of 20

customers has a mean of 1.7 minutes with a standard

deviation of 0.8 minute. If α = 0.05, test the fast food

outlet's claim using P-values.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

19.

A fast food outlet claims that the mean waiting time in

line is less than 3.5 minutes. A random sample of 20

customers has a mean of 3.7 minutes with a standard

deviation of 0.8 minute. If α = 0.05, test the fast food

outlet's claim.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

20.

A fast food outlet claims that the mean waiting time in

line is less than 3.5 minutes. A random sample of 20

customers has a mean of 3.7 minutes with a standard

deviation of 0.8 minute. If α = 0.05, test the fast food

outlet's claim.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

21.

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. A 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 null hypothesis.

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

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

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

22.

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

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

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

23.

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.

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

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

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

24.

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

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

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

25.

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.

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

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

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

26.

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

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

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

27.

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.

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

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

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

28.

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

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

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

29.

In a random sample of 1000 adult Americans, 700 indicated that they oppose the reinstatement of a military draft. Is there convincing evidence that the proportion of American adults who oppose the reinstatement of the draft is different from two-thirds? State the null hypothesis.

H_o: p < 2/3, where p is the true proportion of American adults who oppose the reinstatement of the draft.

H_o: p > 2/3, where p is the true proportion of American adults who oppose the reinstatement of the draft.

H_o: p = 2/3, where p is the true proportion of American adults who oppose the reinstatement of the draft.

30.

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

31.

In a recent survey, the average amount of money

students have in their pockets is $5.40 with a standard

deviation of $1.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

$5.50. At α = 0.05, test the teacher’s claim that the

average amount of money is actually higher than $5.40.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

32.

In a recent survey, the average amount of money

students have in their pockets is $5.40 with a standard

deviation of $1.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

$5.50. At α = 0.05, test the teacher’s claim that the

average amount of money is actually higher than $5.40.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

33.

The average miles on a tank of gas for the Ford

Explorer is 300 miles with a standard deviation of 22

miles. A consumer group feels the average is actually

lower. They survey 40 vehicles and find the average

miles per tank is 290 miles. At α = 0.05, test the

consumer groups’ claim that the miles per tank is

actually lower than 300 miles.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

34.

A sample of 35 cans of Campbell’s Tomato Soup found

that the net weight of the cans was 298 grams with a

standard deviation of 24 grams. The production line

supervisor has been told that the net weight of all cans

is 308 grams. Is there enough evidence, at the 5% level,

to say that the weight of the cans is something other

than 308 grams?

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

35.

A sample of 35 cans of Campbell’s Tomato Soup found

that the net weight of the cans was 298 grams with a

standard deviation of 24 grams. The production line

supervisor has been told that the net weight of all cans

is 308 grams. Is there enough evidence, at the 5% level,

to say that the weight of the cans is something other

than 308 grams?

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

36.

The Quick Stop claims that the Big Slurp will contain 48

ounces of drink. You decide to test this claim because

you feel the actual amount is lower. Over the next few

weeks, you buy 50 Big Slurps and find the average

amount of drink is 47 ounces with a standard deviation

of 2.75 ounces. At α = 0.05, can you reject the Quick

Stop’s claim?

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

37.

A manufacturer claims that his tires last at least 40,000

miles. A test on 25 tires reveals that the mean life of a tire

is 39,750 miles, with a standard deviation of 387 miles.

Test the Manufacturer’s claim at α = .01.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

38.

In a recent survey, the average amount of money

students have in their pockets is $5.40 with a standard

deviation of $1.20. A teacher feels that the average

amount is actually higher. She surveys 80 randomly

selected students and finds the average amount is

$5.50. At α = 0.05, test the teacher’s claim that the

average amount of money is actually higher than $5.40.

Reject Ho

Reject Ha

Fail to reject Ho

Fail to reject Ha

39.

The average miles on a tank of gas for the Ford

Explorer is 300 miles with a standard deviation of 22

miles. A consumer group feels the average is actually

lower. They survey 40 vehicles and find the average

miles per tank is 290 miles. At α = 0.05, test the

consumer groups’ claim that the miles per tank is

actually lower than 300 miles.

There is enough evidence to reject the claim

There is not enough evidence to reject the claim

There is enough evidence to support the claim

There is not enough evidence to support the claim

40.

Ho: p=.21
Ha: p > .21

Ho: p< .21
Ha: p= .21

Ho: p> .21
Ha: p= .21

Ho: p= .21
Ha: p< .21

41.

5% of trucks of a certain model have needed new engines after being driven between 0 and 100 miles. The manufacturer hopes that the redesign of one of the engine's components has solved this problem. Write the null and alternative hypotheses for this situation.

Ho: p< 0.05
Ha: p = 0.05

Ho: p = 0.05
Ha: p > 0.05

Ho: p = 0.05
Ha: p < 0.05

Ho: p > 0.05
Ha: p = 0.05

42.

A state university wants to increase it retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluates it retention rate and comes up with a P-value of 0.075. What is a reasonable conclusion?

There is a92.5% chance of the new programs having no effect on retention.

There is a 7.5% chance of the new programs having no effect on retention.

We can say there is a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. There is no evidence the new programs are more effective, but we cannot conclude that they have no effect on retention.

There's only a 7.5% chance of seeing the new programs having no effect on retention in the results we observed from natural sampling variation. We conclude the new programs are more effective.

43.

A company hopes to improve its engines, setting a goal of no more than 3% of customers using their warranty on defective engine parts. A random survey of 1200 customers found only 20 with complaints. Create a 95% confidence interval for the true level of warranty users among all customers.

Based on the data we are 95% confident the proportion of warranty users is between 0.9% and 2.4%. Therefore the company met its goal.

Based on the data we are 95% confident the proportion of warranty users is between 2.0% and 2.4%. Therefore the company has met its goal.

Based on the data we are 95% confident the proportion of warranty users is between 0.9% and 3.8%. therefore, the company has not met its goal.

Based on the data we are 95% confident the proportion of warranty users is between 0% and 2.4%. Therefore, the company has met its goal.

44.

A state university wants to increase its retention rate of 4% for graduating students from the previous year. After implementing several new programs during the last two years, the university reevaluated its retention rate using a random sample of 352 students and found the retention rate at 5%. Test the appropriate hypothesis and state your conclusion. Be sure to check assumptions and conditions.

Ho: p = .04; Ha: p> .04; z = 0.96; P-value = 0.1685. This data does not show that more than 4% of students are retained; they should not continue with the new programs.

Ho: p = .04; Ha: p<.04; z = -1.07; P-value =0.8577. This data shows that more than 4% of the students are retained; the university should continue with the new programs.

Ho: p = .04; Ha: p ≠ .04; z = 1.07; P-value = 0.2846; This data does not show that more than 4% of students are retained; the university should not continue with the new programs.

45.

A P-value indicates:

the probability that the null hypothesis is true

the probability that the alternative hypothesis is true

the probability of the observed statistic given the null hypothesis is true

the probability that the null is true given the observed statistic

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Hypothesis Testing 1

Total questions: 45

Worksheet time: 1hrs 9mins

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