1.)Find the complement of the claim.

>406

Which is H0 and which is Ha?

2.)Use the given statement to represent a claim. Write its complement and state which is H0 and which is Ha.

p>0.57

Find the complement of the claim.

3.)A refrigerator manufacturer claims that the mean life of its competitor's refrigerators is less than 13 years. You are asked to perform a hypothesis test to test this claim.

(a) How would you write the null and alternative hypothesis if you represent the manufacturer and want to support the claim?

(b) How would you write the null and alternative hypothesis if you represent the competitor and want to reject the claim?

H0:

mu

sigma

sigma squared2

pp

greater than>

not equals

less than<

greater than or equals

less than or equals

13

Ha:

greater than>

not equals

greater than or equals

less than<

less than or equals

13

4.)Find the P-value for the indicated hypothesis test with the given standardized test statistic, z. Decide whether to reject H0 for the given level of significance .

Right-tailed test with test statistic z=1.74 and =0.09

P-value=_____enter your response here (Round to four decimal places as needed.)

5.)Match each P-value with the graph that displays its area without performing any calculations. Explain your reasoning. P=0.0119 and P=0.2483.

-3

0

3

z

z

(a) z=2.26

A graph labeled (a) has a normal curve above and centered on the 0 of a horizontal axis labeled from negative 3 to 3 in increments of 1. A vertical line segment extends from the curve to the horizontal axis at the labeled point z is equal to negative 2.26. The area under the curve to the left of z is shaded.

-3

0

3

z

z

(b) z=0.68

A graph labeled (b) has a normal curve above and centered on the 0 of a horizontal axis labeled from negative 3 to 3 in increments of 1. A vertical line segment extends from the curve to the horizontal axis at the labeled point z is equal to negative 0.68. The area under the curve to the left of z is shaded.

Graph

(a)

(b)

displays the area for P=0.0119 and graph

(a)

(b)

displays the area for P=0.2483 because the P-value

is equal to one minus

is related to one minus

is equal to

is related to

the

absolute value of z.

shaded area.

6.)Find the critical value(s) for a left-tailed z-test with =0.09. Include a graph with your answer.

The critical value(s) is(are)_____ enter your response here.

(Round to two decimal places as needed. Use a comma to separate answers as needed.)

7.)Test the claim about the population mean, , at the given level of significance using the given sample statistics.

Claim: =50; =0.05; =3.48. Sample statistics: x=49.9, n=51

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

H0: =50

Ha: 50

B.

H0: <50

Ha: =50

C.

H0: =50

Ha: <50

D.

H0: 50

Ha: =50

E.

H0: >50

Ha: =50

F.

H0: =50

Ha: >

8.)A random sample of 79 eighth grade students' scores on a national mathematics assessment test has a mean score of 282. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 275. Assume that the population standard deviation is 31. At =0.11, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).

(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.

A.

H0: 275 (claim)

Ha: <275

B.

H0: 275

Ha: >275 (claim)

C.

H0: =275

Ha: >275 (claim)

D.

H0: <275

Ha: 275 (claim)

E.

H0: 275 (claim)

Ha: >275

F.

H0: =275 (claim)

Ha: >275

9.)A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 916 milligrams. A random sample of 47 breakfast sandwiches has a mean sodium content of 910 milligrams. Assume the population standard deviation is 19 milligrams. At =0.10, do you have enough evidence to reject the restaurant's claim? Complete parts (a) through (e).

(a) Identify the null hypothesis and alternative hypothesis.

A.

H0: <910 (claim)

Ha: 910

B.

H0: 916 (claim)

Ha: =916

C.

H0: >916

Ha: 916 (claim)

D.

H0: =910 (claim)

Ha: 910

E.

H0: 916 (claim)

Ha: >916

F.

H0: 910

Ha: <910 (claim)

10.)You are given the sample mean and the population standard deviation. Use this information to construct the 90% and 95% confidence intervals for the population mean. Interpret the results and compare the widths of the confidence intervals.

From a random sample of 36 business days, the mean closing price of a certain stock was $116.69. Assume the population standard deviation is $10.80.

The 90% confidence interval is (enter your response here,enter your response here).

(Round to two decimal places as needed.)

The 95% confidence interval is (enter your response here,enter your response here).

(Round to two decimal places as needed.)

Which interval is wider? Choose the correct answer below.

The 95% confidence interval

The 90% confidence interval

Interpret the results.

A.

You can be certain that the population mean price of the stock is either between the lower bounds of the 90% and 95% confidence intervals or the upper bounds of the 90% and 95% confidence intervals.

B.

You can be certain that the closing price of the stock was within the 90% confidence interval for approximately 32 of the 36 days, and was within the 95% confidence interval for approximately 34 of the 36 days.

C.

You can be 90% confident that the population mean price of the stock is outside the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

D.

You can be 90% confident that the population mean price of the stock is between the bounds of the 90% confidence interval, and 95% confident for the 95% interval.

11.)Determine the minimum sample size required when you want to be 90% confident that the sample mean is within one unit of the population mean and =11.5. Assume the population is normally distributed.

A 90% confidence level requires a sample size of enter your response here.

(Round up to the nearest whole number as needed.)

12.)Assume the random variable x is normally distributed with mean =80 and standard deviation =4. Find the indicated probability.

P(x<73)

P(x<73)=enter your response here (Round to four decimal places as needed.)

13.)Find the area of the shaded region under the standard normal curve. If convenient, use technology to find the area.

z

-2.22

0

A normal curve is over a horizontal z-axis and is centered at 0. Vertical line segments extend from the horizontal axis to the curve at negative 2.22 and 0. The area under the curve between negative 2.22 and 0 is shaded.

The area of the shaded region is enter your response here.

(Round to four decimal places as needed.)

13.)Find the z-score that has 69.1% of the distribution's area to its right.

The z-score is enter your response here.

(Round to two decimal places as needed.)

14.)Find the critical value zc necessary to form a confidence interval at the level of confidence shown below.

c=0.97

zc=enter your response here

(Round to two decimal places as needed.)

15.)Find the margin of error for the given values of c, , and n.

c=0.90, =3.2, n=64

LOADING... Click the icon to view a table of common critical values.

E=enter your response here (Round to three decimal places as needed.)Level of Confidence

zc

90%

1.645

95%

1.96

99%

2.575

16.)The mean height of women in a country (ages 2029) is 63.6 inches. A random sample of 60 women in this age group is selected. What is the probability that the mean height for the sample is greater than 64 inches? Assume =2.94.

The probability that the mean height for the sample is greater than 64 inches is enter your response here.

(Round to four decimal places as needed.)

17.)In a recent study on world happiness, participants were asked to evaluate their current lives on a scale from 0 to 10, where 0 represents the worst possible life and 10 represents the best possible life. The responses were normally distributed, with a mean of 4.7 and a standard deviation of 2.5. Answer parts (a)-(d) below.

(a) Find the probability that a randomly selected study participant's response was less than 4.

The probability that a randomly selected study participant's response was less than 4 is enter your response here. (Round to four decimal places as needed.)

(b) Find the probability that a randomly selected study participant's response was between 4 and 6.

The probability that a randomly selected study participant's response was between 4 and 6 is enter your response here. (Round to four decimal places as needed.)

(c) Find the probability that a randomly selected study participant's response was more than 8.

The probability that a randomly selected study participant's response was more than 8 is enter your response here. (Round to four decimal places as needed.)

(d) Identify any unusual events. Explain your reasoning. Choose the correct answer below.

A.

The event in part (a) is unusual because its probability is less than 0.05.

B.

The events in parts (a) and (c) are unusual because their probabilities are less than 0.05.

C.

There are no unusual events because all the probabilities are greater than 0.05.

D.

The events in parts (a), (b), and (c) are unusual because all of their probabilities are less than 0.05.

18.)Find the indicated area under the standard normal curve.

To the left of z=0.26

Click here to view page 1 of the standard normal table. LOADING...

Click here to view page 2 of the standard normal table. LOADING...

The area to the left of z=0.26 under the standard normal curve is enter your response here.

(Round to four decimal places as needed.)

19.)Find the indicated z-score shown in the graph to the right.

z

Area=0.2546z=?

0

A normal curve is over a horizontal z-axis and is centered on 0. A vertical line segment extends from the curve to the horizontal axis at a point labeled z = ?. The area under the curve and to the left of the vertical line segment is shaded and labeled Area = 0.2546.

The z-score is enter your response here.

(Round to two decimal places as needed.)

20.)Assume a member is selected at random from the population represented by the graph. Find the probability that the member selected at random is from the shaded area of the graph. Assume the variable x is normally distributed.

SAT Critical Reading Scores

200

800

475

Score

=506=122200

x

A graph titled S A T Critical Reading Scores has a normal curve over a horizontal x-axis labeled Score from less than 200 to more than 800. Vertical line segments extend from the horizontal axis to the curve at 200 and 475, where 475 is to the left of center. The area under the curve between 200 and 475 is shaded and labeled 200 less than x less than 475. The equations mu equals 506 and sigma equals 122 are displayed on the graph.

The probability that the member selected at random is from the shaded area of the graph is enter your response here. (Round to four decimal places as needed.)

20.)The red blood cell counts (in millions of cells per microliter) for a population of adult males can be approximated by a normal distribution, with a mean of 5.5 million cells per microliter and a standard deviation of 0.5 million cells per microliter.

(a) What is the minimum red blood cell count that can be in the top 25% of counts?

(b) What is the maximum red blood cell count that can be in the bottom 15% of counts?

(a) The minimum red blood cell count is enter your response here million cells per microliter.

(Round to two decimal places as needed.)

(b) The maximum red blood cell count is enter your response here million cells per microliter.

(Round to two decimal places as needed.)

21.)Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.

Claim: 1160; =0.07; =206.26. Sample statistics: x=1192.96, n=250

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

H0: >1160

Ha: 1160

B.

H0: 1160

Ha: >1160

C.

H0: >1192.96

Ha: 1192.96

D.

H0: 1192.96

Ha: <1192.96

E.

H0: 1160

Ha: <1160

F.

H0: 1192.96

Ha: >1192.96

Calculate the standardized test statistic.

The standardized test statistic is enter your response here.

(Round to two decimal places as needed.)

Determine the P-value.

P=enter your response here (Round to three decimal places as needed.)

Determine the outcome and conclusion of the test.

Fail to reject

Reject

H0. At the 7% significance level, there

is

is not

enough evidence to

support

reject

the claim.

22.)A random sample of 85 eighth grade students' scores on a national mathematics assessment test has a mean score of 287. This test result prompts a state school administrator to declare that the mean score for the state's eighth graders on this exam is more than 280. Assume that the population standard deviation is 34. At =0.13, is there enough evidence to support the administrator's claim? Complete parts (a) through (e).

(a) Write the claim mathematically and identify H0 and Ha. Choose the correct answer below.

A.

H0: 280 (claim)

Ha: >280

B.

H0: =280 (claim)

Ha: >280

C.

H0: <280

Ha: 280 (claim)

D.

H0: 280 (claim)

Ha: <280

E.

H0: 280

Ha: >280 (claim)

F.

H0: =280

Ha: >280 (claim)

(b) Find the standardized test statistic z, and its corresponding area.

z=enter your response here (Round to two decimal places as needed.)

(c) Find the P-value.

P-value=enter your response here (Round to three decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Fail to reject H0

Reject H0

(e) Interpret your decision in the context of the original claim.

At the 13% significance level, there

is

is not

enough evidence to

support

reject

the administrator's claim that the mean score for the state's eighth graders on the exam is more than 280.

23.)A nutritionist claims that the mean tuna consumption by a person is 3.1 pounds per year. A sample of 70 people shows that the mean tuna consumption by a person is 2.9 pounds per year. Assume the population standard deviation is 1.22 pounds. At =0.02, can you reject the claim?

(a) Identify the null hypothesis and alternative hypothesis.

A.

H0: 2.9

Ha: =2.9

B.

H0: >3.1

Ha: 3.1

C.

H0: >2.9

Ha: 2.9

D.

H0: 3.1

Ha: >3.1

E.

H0: 2.9

Ha: >2.9

F.

H0: =3.1

Ha: 3.1

(b) Identify the standardized test statistic.

z=enter your response here (Round to two decimal places as needed.)

(c) Find the P-value.

enter your response here (Round to three decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

A.

Reject H0. There is sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds.

B.

Fail to reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds.

C.

Reject H0. There is not sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds.

D.

Fail to reject H0. There is sufficient evidence to reject the claim that mean tuna consumption is equal to 3.1 pounds.

24.)A company that makes cola drinks states that the mean caffeine content per 12-ounce bottle of cola is 55 milligrams. You want to test this claim. During your tests, you find that a random sample of thirty 12-ounce bottles of cola has a mean caffeine content of 55.6 milligrams. Assume the population is normally distributed and the population standard deviation is 7.9 milligrams. At =0.10, can you reject the company's claim? Complete parts (a) through (e).

(a) Identify H0 and Ha. Choose the correct answer below.

A.

H0: 55.6

Ha: =55.6

B.

H0: 55

Ha: <55

C.

H0: =55.6

Ha: 55.6

D.

H0: =55

Ha: 55

E.

H0: 55.6

Ha: <55.6

F.

H0: 55

Ha: =55

(b) Find the critical value(s). Select the correct choice below and fill in the answer box within your choice.

(Round to two decimal places as needed.)

A.

The critical values are enter your response here.

B.

The critical value is enter your response here.

Identify the rejection region(s). Choose the correct answer below.

A.

-4

0

4

z

Reject H0.Reject H0.Fail to reject H0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend to the left of and to the right 0 from the horizontal axis to the curve. The area under the curve the left of the left line segment and to the right of the right lines segment is shaded and labeled Reject H@Sub{0}. The area between the vertical line segments is labeled Fail to reject H@Sub{0}.

B.

-4

0

4

z

Reject H0.Fail to reject H0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the left of 0 from the horizontal axis to the curve. The area under the curve to the left of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the right of the line segment is labeled Fail to reject H@Sub{0}.

C.

-4

0

4

z

Reject H0.Fail to reject H0.

A normal curve is over a horizontal axis labeled z from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segment extends to the right of 0 from the horizontal axis to the curve. The area under the curve to the right of the line segment is shaded and labeled Reject H@Sub{0}. The area under the curve to the left of the line segment is labeled Fail to reject H@Sub{0}.

(c) Find the standardized test statistic.

z=enter your response here (Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

A.

Since z is in the rejection region, fail to reject the null hypothesis.

B.

Since z is in the rejection region, reject the null hypothesis.

C.

Since z is not in the rejection region, fail to reject the null hypothesis.

D.

Since z is not in the rejection region, reject the null hypothesis.

(e) Interpret the decision in the context of the original claim.

At the 10% significance level, there

is not

is

enough evidence to

reject

support

the company's claim that the mean caffeine content per 12-ounce bottle of cola

is equal to

is greater than

is different from

is less than

enter your response here milligrams.

25.)A fast food restaurant estimates that the mean sodium content in one of its breakfast sandwiches is no more than 918 milligrams. A random sample of 60 breakfast sandwiches has a mean sodium content of 913 milligrams. Assume the population standard deviation is 23 milligrams. At =0.10, do you have enough evidence to reject the restaurant's claim? Complete parts (a) through (e).

(a) Identify the null hypothesis and alternative hypothesis.

A.

H0: 913

Ha: <913 (claim)

B.

H0: 918 (claim)

Ha: >918

C.

H0: <913 (claim)

Ha: 913

D.

H0: 918 (claim)

Ha: =918

E.

H0: =913 (claim)

Ha: 913

F.

H0: >918

Ha: 918 (claim)

(b) Identify the critical value(s). Use technology.

z0=enter your response here

(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Identify the rejection region(s). Select the correct choice below.

A.

The rejection region is z>1.28.

B.

The rejection regions are z>1.28 and z<1.28.

C.

The rejection region is z<1.28.

(c) Identify the standardized test statistic. Use technology.

z=enter your response here (Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

A.

Reject H0. There is not sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams.

B.

Reject H0. There is sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams.

C.

Fail to reject H0. There is sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams.

D.

Fail to reject H0. There is not sufficient evidence to reject the claim that mean sodium content is no more than 918 milligrams.

26.)Use technology to help you test the claim about the population mean, , at the given level of significance, , using the given sample statistics. Assume the population is normally distributed.

Claim: >1240; =0.03; =213.07. Sample statistics: x=1257.23, n=300

Identify the null and alternative hypotheses. Choose the correct answer below.

A.

H0: 1257.23

Ha: <1257.23

B.

H0: 1257.23

Ha: >1257.23

C.

H0: 1240

Ha: <1240

D.

H0: 1240

Ha: >1240

E.

H0: >1257.23

Ha: 1257.23

F.

H0: >1240

Ha: 1240

Calculate the standardized test statistic.

The standardized test statistic is enter your response here.

(Round to two decimal places as needed.)

Determine the P-value.

P=enter your response here (Round to three decimal places as needed.)

Determine the outcome and conclusion of the test.

Fail to reject

Reject

H0. At the 3% significance level, there

is

is not

enough evidence to

reject

support

the claim.

27.)

A light bulb manufacturer guarantees that the mean life of a certain type of light bulb is at least 764 hours. A random sample of 23 light bulbs has a mean life of 744 hours. Assume the population is normally distributed and the population standard deviation is 61 hours. At =0.08, do you have enough evidence to reject the manufacturer's claim? Complete parts (a) through (e).

(a) Identify the null hypothesis and alternative hypothesis.

A.

H0: >764

Ha: 764 (claim)

B.

H0: =744

Ha: 744 (claim)

C.

H0: 764(claim)

Ha: =764

D.

H0: 764 (claim)

Ha: <764

E.

H0: 744

Ha: >744 (claim)

F.

H0: <744 (claim)

Ha: 744

(b) Identify the critical value(s). Use technology.

z0=enter your response here

(Use a comma to separate answers as needed. Round to two decimal places as needed.)

Identify the rejection region(s). Choose the correct answer below.

A.

-4

0

4

z

Reject H0.Fail to reject H0.

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. A vertical line segment extends from the horizontal axis to the curve at 1.4. The area under the curve to the right of 1.4 is shaded one color and labeled Reject Upper H 0. The area under the curve to the left of 1.4 is shaded another color and labeled Fail to reject Upper H 0.

B.

-4

0

4

z

Reject H0.Reject H0.Fail to reject H0.

A normal curve is over a horizontal z-axis labeled from negative 4 to 4 in increments of 1 and is centered on 0. Vertical line segments extend from the horizontal axis to the curve at negative 1.4 and 1.4. The area under the curve to the left of negative 1.4 is shaded and the area under the curve to the right of 1.4 are both shaded one color and labeled Reject Upper H 0.The area under the curve between negative 1.4 and 1.4 is shaded another color and labeled Fail to reject Upper H 0.

C.

-4

0

4

z

Reject H0.Fail to reject H0.

(c) Identify the standardized test statistic. Use technology.

z=enter your response here (Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the decision in the context of the original claim.

A.

Reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 764 hours.

B.

Reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 764 hours.

C.

Fail to reject H0. There is not sufficient evidence to reject the claim that mean bulb life is at least 764 hours.

D.

Fail to reject H0. There is sufficient evidence to reject the claim that mean bulb life is at least 764 hours.

28.)A scientist estimates that the mean nitrogen dioxide level in a city is greater than 33 parts per billion. To test this estimate, you determine the nitrogen dioxide levels for 31 randomly selected days. The results (in parts per billion) are listed to the right. Assume that the population standard deviation is 7. At =0.11, can you support the scientist's estimate? Complete parts (a) through (e).

20

23

41

17

39

38

31

39

28

19

26

22

29

23

40

41

44

21

17

44

19

34

21

36

36

32

44

16

18

22

25

(a) Write the claim mathematically and identify H0 and Ha. Choose from the following.

A.

H0: <33

Ha: 33 (claim)

B.

H0: 33 (claim)

Ha: <33

C.

H0: 33 (claim)

Ha: >33

D.

H0: 33

Ha: >33 (claim)

E.

H0: =33

Ha: >33 (claim)

F.

H0: =33 (claim)

Ha: >33

(b) Find the critical value and identify the rejection region.

z0=enter your response here (Round to two decimal places as needed.)

Rejection region: z

greater than>

less than<

enter your response here

(c) Find the standardized test statistic.

z=enter your response here (Round to two decimal places as needed.)

(d) Decide whether to reject or fail to reject the null hypothesis.

Reject H0

Fail to reject H0

(e) Interpret the decision in the context of the original claim.

At the 11% significance level, there

is not

is

enough evidence to

support

reject

the scientist's claim that the mean nitrogen dioxide level in the city is greater than 33 parts per billion.