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Student: Jorge Ithier

Date: 12/6/16

Instructor: Alexandra Wrigley

Course: Statistics for Decision Making

(100)

Assignment: Week 7 Homework 40 pts

A null and alternative hypothesis are given. Determine whether the hypothesis test is left-tailed, right-tailed, or two-tailed.

:H0 p = 0.1

:Ha p ≠ 0.1

What type of test is being conducted in this problem?

A. -tailed testRight

B. -tailed testLeft

C. -tailed testTwo

For the statement below, write the claim as a mathematical statement. State the null and alternative hypotheses and

identify which represents the claim.

A laptop manufacturer claims that the mean life of the battery for a certain model of laptop is hours.more than 7

Write the claim as a mathematical statement.

A. ≥ 7 B. ≠ 7 C. > 7

D. < 7 E. ≤ 7 F. = 7

Choose the correct null and alternative hypotheses below.

A. :H0 ≥ 7

:Ha < 7

B. :H0 = 7

:Ha ≠ 7

C. :H0 < 7

:Ha ≥ 7

D. :H0 ≠ 7

:Ha = 7

E. :H0 ≤ 7

:Ha > 7

F. :H0 > 7

:Ha ≤ 7

Identify which is the claim.

A. The null hypothesis : is the claimH0 ≥ 7

C. The null hypothesis : is the claim.H0 ≤ 7

D. The alternative hypothesis : is the claim.Ha > 7

E. The alternative hypothesis : is the claimHa ≠ 7

F. The alternative hypothesis : is the claimHa < 7

The null hypothesis : is the claimH0 = 7

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(1) (2) (3)

A security expert claims that % of all homeowners have a home security alarm. State and in words and in

symbols. Then determine whether the hypothesis test for this claim is left-tailed, right-tailed, or two-tailed. Explain your

reasoning.

exactly 11 H0 Ha

State the null hypothesis in words and in symbols. Choose the correct answer below.

A. The null hypothesis expressed in words is, "the proportion of all homeowners who own a

home security alarm is ." The null hypothesis is expressed symbolically as, " :

p ."

at least 0.11 H0

≥ 0.11

B. The null hypothesis expressed in words is, "the proportion of all homeowners who own a

home security alarm is ." The null hypothesis is expressed symbolically as, " :

p ."

at most 0.11 H0

≤ 0.11

C. The null hypothesis expressed in words is, "the proportion of all homeowners who own a

home security alarm is ." The null hypothesis is expressed symbolically as,

" : p ."

more than 0.11

H0 > 0.11

D. The null hypothesis expressed in words is, "the proportion of all homeowners who own a

home security alarm is ." The null hypothesis is expressed symbolically as, " : p ."0.11 H0 = 0.11

State the alternative hypothesis in words and in symbols. Choose the correct answer below.

A. The alternative hypothesis expressed in words is, "the proportion of all homeowners who own

a home security alarm ." The alternative hypothesis is expressed

symbolically as, " : p ."

is more than 0.11

Ha > 0.11

B. The alternative hypothesis expressed in words is, "the proportion of all homeowners who own

a home security alarm ." The alternative hypothesis is expressed

symbolically as, " : p ."

is not equal to 0.11

Ha ≠ 0.11

C. The alternative hypothesis expressed in words is, "the proportion of all homeowners who own

a home security alarm ." The alternative hypothesis is expressed symbolically

as, " : p ."

is less than 0.11

Ha < 0.11

D. The alternative hypothesis expressed in words is, "the proportion of all homeowners who own

a home security alarm ." The alternative hypothesis is expressed symbolically as, " :

p ."

is 0.11 Ha

= 0.11

The hypothesis test is (1) because the (2) contains (3)

left tailed

right tailed

two tailed

null hypothesis

alternative hypothesis

≠ .

≤ .

< .

≥ .

= .

> .

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(1) contains

does not contain

(2) null

alternative

(3) sufficient

insufficient

(4) reject

support

(5) sufficient

insufficient

(6) support

reject

Determine whether the claim stated below represents the null hypothesis or the alternative hypothesis. If a hypothesis test

is performed, how should you interpret a decision that (a) rejects the null hypothesis or (b) fails to reject the null hypothesis?

A scientist claims that the mean incubation period for the eggs of a species of bird is days.more than 53

Does the claim represent the null hypothesis or the alternative hypothesis?

Since the claim (1) a statement of equality, it represents the (2) hypothesis.

(a) How should you interpret a decision that rejects the null hypothesis?

There is (3) evidence to (4) the claim that the mean incubation period for the eggs of a

species of bird is days.more than 53

(b) How should you interpret a decision that fails to reject the null hypothesis?

There is (5) evidence to (6) the claim that the mean incubation period for the eggs of a

species of bird is days.more than 53

Determine whether to reject or fail to reject at the level of significance of a) and b) .H0 = 0.03 = 0.09

: , : , and P .H0 = 144 Ha ≠ 144 = 0.0393

a) Do you reject or fail to reject at the level of significance?H0 0.03

A. because P .Fail to reject H0 < 0.03

B. because P .Fail to reject H0 > 0.03

C. because P .Reject H0 < 0.03

D. because P .Reject H0 > 0.03

b) Do you reject or fail to reject at the level of significance?H0 0.09

A. because P .Reject H0 > 0.09

B. because P .Reject H0 < 0.09

C. because P .Fail to reject H0 > 0.09

D. because P .Fail to reject H0 < 0.09

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The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject when the level of significance is

(a) , (b) , and (c) .

= 0.01 = 0.05 = 0.10

P = 0.0978

(a) Do you reject or fail to reject at the level of significance?H0 0.01

A. because the P-value, , is than .Reject H0 0.0978 less = 0.01

B. because the P-value, , is than .Fail to reject H0 0.0978 greater = 0.01

C. because the P-value, , is than .Reject H0 0.0978 greater = 0.01

D. because the P-value, , is than .Fail to reject H0 0.0978 less = 0.01

(b) Do you reject or fail to reject at the level of significance?H0 0.05

A. because the P-value, , is than .Fail to reject H0 0.0978 greater = 0.05

B. because the P-value, , is than .Reject H0 0.0978 less = 0.05

C. because the P-value, , is than .Reject H0 0.0978 greater = 0.05

D. because the P-value, , is than .Fail to reject H0 0.0978 less = 0.05

A. because the P-value, , is than .Fail to reject H0 0.0978 greater = 0.10

B. because the P-value, , is than .Reject H0 0.0978 greater = 0.10

C. because the P-value, , is than .Fail to reject H0 0.0978 less = 0.10

D. because the P-value, , is than .Reject H0 0.0978 less = 0.10

Determine whether to reject or fail to reject at the level of significance of a) and b) .H0 = 0.05 = 0.06

: , : , and P .H0 = 137 Ha ≠ 137 = 0.0596

a) Do you reject or fail to reject at the level of significance?H0 0.05

A. because P .Fail to reject H0 > 0.05

B. because P .Reject H0 > 0.05

C. because P .Reject H0 < 0.05

D. because P .Fail to reject H0 < 0.05

b) Do you reject or fail to reject at the level of significance?H0 0.06

A. because P .Fail to reject H0 < 0.06

B. because P .Reject H0 > 0.06

C. because P .Reject H0 < 0.06

D. because P .Fail to reject H0 > 0.06

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(1) Fail to reject

Reject

(2) is

is not

(3) support

reject

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: ; ; . Sample statistics: , n> 1200 = 0.01 = 200.35 x = 1219.46 = 250

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

A. :H0 ≤ 1200

:Ha > 1200

B. :H0 ≤ 1219.46

:Ha > 1219.46

C. :H0 > 1200

:Ha ≤ 1200

D. :H0 ≥ 1200

:Ha < 1200

E. :H0 ≥ 1219.46

:Ha < 1219.46

F. :H0 > 1219.46

:Ha ≤ 1219.46

Calculate the standardized test statistic.

The standardized test statistic is .

(Round to two decimal places as needed.)

Determine the P-value.

P (Round to three decimal places as needed.)=

Determine the outcome and conclusion of the test.

(1) . At the % significance level, there (2) enough evidence to

(3) the claim.

H0 1

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(1) is

is not

(2) support

reject

A random sample of eighth grade students' scores on a national mathematics assessment test has a mean score of

. 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 . Assume that the population standard deviation is . At , is there enough evidence to

support the administrator's claim? Complete parts (a) through (e).

269

260 37 = 0.08

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

A. : (claim)H0 ≥ 260

:Ha < 260

B. : (claim)H0 = 260

:Ha > 260

C. :H0 ≤ 260

: (claim)Ha > 260

D. :H0 < 260

: (claim)Ha ≥ 260

E. :H0 = 260

: (claim)Ha > 260

F. : (claim)H0 ≤ 260

:Ha > 260

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

z (Round to two decimal places as needed.)=

P-value (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 % significance level, there (1) enough evidence to (2) the administrator's claim

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

260

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10. The lengths of time (in years) it took a random sample of former smokers to quit smoking permanently are listed.

Assume the population standard deviation is years. At , is there enough evidence to reject the claim that the

mean time it takes smokers to quit smoking permanently is years? Complete parts (a) through (e).

6.5 = 0.01

16.8 22.4 9.9 19.6 21.6 21.9 13.5 12.4

17.9 15.4 11.2 22.8 13.1 9.4 13.6 15.6

8.6 22.8 9.8 14.1 22.4 8.5 9.4 19.6

19.7 16.9 19.3 7.3 14.6 21.6 16.8 10.7

(a) Identify the claim and state the null hypothesis and alternative hypothesis.

A. : (claim)H0 ≤ 14

:Ha > 14

B. : (claim)H0 ≥ 14

:Ha < 14

C. : (claim)H0 > 14

:Ha ≤ 14

D. : (claim)H0 ≠ 14

:Ha = 14

E. : (claim)H0 = 14

:Ha ≠ 14

F. :H0 > 14

: (claim)Ha ≤ 14

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

z (Round to two decimal places as needed.)=

P (Round to three 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 at the % level of significance.1

A. . There sufficient

evidence to reject the claim that the

mean time it takes smokers to quit

smoking permanently is years.

Fail to reject H0 is

B. . There sufficient

evidence to reject the claim that the

mean time it takes smokers to quit

smoking permanently is years.

Fail to reject H0 is not

C. . There sufficient

evidence to reject the claim that the

mean time it takes smokers to quit

smoking permanently is years.

Reject H0 is not

D. . There sufficient evidence to

reject the claim that the mean time it

takes smokers to quit smoking

permanently is years.

Reject H0 is

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11.

12.

Use technology and a t-test to 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: ; Sample statistics: , s , n> 72 = 0.10 x = 74.9 = 3.4 = 25

What are the null and alternative hypotheses? Choose the correct answer below.

A. H0: ≤ 72

HA: > 72

B. H0: ≠ 72

HA: = 72

C. H0: = 72

HA: ≠ 72

D. H0: ≥ 72

HA: < 72

What is the value of the standardized test statistic?

The standardized test statistic is . (Round to two decimal places as needed.)

What is the P-value of the test statistic?

P-value (Round to three decimal places as needed.)=

Decide whether to reject or fail to reject the null hypothesis. Choose the correct answer below.

A. . There enough evidence to support the claim.Reject H0 is

B. . There enough evidence to support the claim.Fail to reject H0 is

C. . There enough evidence to support the claim.Reject H0 is not

D. . There enough evidence to support the claim.Fail to reject H0 is not

Use a t-test to 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: ; Sample statistics: , s , n≠ 26 = 0.10 x = 28.7 = 4.6 = 11

What are the null and alternative hypotheses? Choose the correct answer below.

A. H0: ≤ 26

Ha: > 26

B. H0: = 26

Ha: ≠ 26

C. H0: ≥ 26

Ha: < 26

D. H0: ≠ 26

Ha: = 26

What is the value of the standardized test statistic?

The standardized test statistic is . (Round to two decimal places as needed.)

What is the P-value of the test statistic?

P-value (Round to three decimal places as needed.)=

Decide whether to reject or fail to reject the null hypothesis.

B. . There enough evidence to support the claim.Reject H0 is not

C. . There enough evidence to support the claim.Fail to reject H0 is not

D. . There enough evidence to support the claim.Reject H0 is

. There enough evidence to support the claim.Fail to reject H0 is

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13. You receive a brochure from a large university. The brochure indicates that the mean class size for full-time faculty is

fewer than students. You want to test this claim. You randomly select classes taught by full-time faculty and

determine the class size of each. The results are shown in the table below. At , can you support the university's

claim? Complete parts (a) through (d) below. Assume the population is normally distributed.

32 18

= 0.10

34 31 31 36 34 39 23 26 29

29 30 35 30 27 26 27 27 26

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

Which of the following correctly states and ?H0 Ha

A. :H0 > 32

:Ha ≤ 32

B. :H0 ≥ 32

:Ha < 32

C. :H0 ≤ 32

:Ha > 32

D. :H0 < 32

:Ha ≥ 32

E. :H0 = 32

:Ha ≠ 32

F. :H0 = 32

:Ha < 32

(b) Use technology to find the P-value.

P (Round to three decimal places as needed.)=

Which of the following is correct?

A. because the P-value is than the significance level.Fail to reject H0 greater

B. because the P-value is than the significance level.Fail to reject H0 less

C. because the P-value is than the significance level.Reject H0 less

D. because the P-value is than the significance level.Reject H0 greater

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

A. At the % level of significance, there

sufficient evidence to support the

claim that the mean class size for

full-time faculty is fewer than students.

is not

B. At the % level of significance, there

sufficient evidence to support the claim

that the mean class size for full-time

faculty is more than students.

10 is

C. At the % level of significance, there

sufficient evidence to support the

claim that the mean class size for

full-time faculty is more than students.

is not

D. At the % level of significance, there

sufficient evidence to support the claim

that the mean class size for full-time

faculty is fewer than students.

10 is

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14. The dean of a university estimates that the mean number of classroom hours per week for full-time faculty is . As a

member of the student council, you want to test this claim. A random sample of the number of classroom hours for eight

full-time faculty for one week is shown in the table below. At , can you reject the dean's claim? Complete parts (a)

through (d) below. Assume the population is normally distributed.

11.0

= 0.10

10.8 7.2 12.9 6.2 7.1 11.3 14.9 8.9

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

Which of the following correctly states and ?H0 Ha

A. :H0 > 11.0

:Ha ≤ 11.0

B. :H0 = 11.0

:Ha ≠ 11.0

C. :H0 ≥ 11.0

:Ha < 11.0

D. :H0 ≤ 11.0

:Ha > 11.0

E. :H0 ≠ 11.0

:Ha = 11.0

F. :H0 < 11.0

:Ha ≥ 11.0

(b) Use technology to find the P-value.

P (Round to three decimal places as needed.)=

Which of the following is correct?

A. because the P-value is the significance level.Fail to reject H0 less than

B. because the P-value is the significance level.Reject H0 greater than

C. because the P-value is the significance level.Fail to reject H0 greater than

D. because the P-value is the significance level.Reject H0 less than

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

A. At the % level of significance, there

sufficient evidence to reject the claim that

the mean number of classroom hours per

week for full-time faculty is

10 is

greater than

11.0

B. At the % level of significance, there

sufficient evidence to reject the

claim that the mean number of

classroom hours per week for full-time

faculty is .

is not

less than 11.0

C. At the % level of significance, there

sufficient evidence to reject the claim that

the mean number of classroom hours per

week for full-time faculty is .

10 is

11.0

D. At the % level of significance, there

sufficient evidence to reject the

claim that the mean number of

classroom hours per week for full-time

faculty is .

is not

11.0

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15. A humane society claims that less than % of U.S. households own a dog. In a random sample of U.S. households,

say they own a dog. At , is there enough evidence to support the society's claim?

38 390

152 = 0.01

(a) Write the claim mathematically and identify and . (b) Find the critical value(s) and identify the rejection region(s).

(c) Find the standardized test statistic. (d) Decide whether to reject or fail to reject the null hypothesis, and (e) interpret the

decision in the context of the original claim.

H0 Ha

(a) Which of the following correctly states and ?H0 Ha

A. : pH0 < 0.38

: pHa ≥ 0.38

B. : pH0 = 0.38

: pHa ≠ 0.38

C. : pH0 ≥ 0.38

: pHa < 0.38

D. : pH0 ≤ 0.38

: pHa > 0.38

(b) What is (are) the critical value(s)?

The critical value(s) is/are .

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

Which of the following graphs has the rejection region(s) shaded correctly?

A. B. C.

z (Round to two decimal places as needed.)=

(d) Which of the following is the correct conclusion for the test?

H0.Reject

H0.Fail to reject

(e) Interpret your results. Choose the correct answer below.

A. There enough evidence to support

the claim that less than % of U.S.

households own a dog.

is not

B. There enough evidence to support the

claim that % of U.S. households own a

dog.

C. There enough evidence to support

the claim that % of U.S. households

own a dog.

is not

D. There enough evidence to support the

claim that less than % of U.S.

households own a dog.

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*16. One study, based on responses from randomly selected teenagers, concluded that % of teenagers cite grades

as their greatest source of pressure. Use a 0.05 significance level to test the claim that fewer than half of all teenagers in

the population feel that grades are their greatest source of pressure.

1,016 41

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

A. : p 0.5H0 =

: p 0.5Ha >

B. : p 0.5H0 =

: p 0.5Ha ≠

C. : p 0.5H0 =

: p 0.5Ha <

D. : p 0.5H0 <

: p 0.5Ha =

Find the test statistic.

z (Round to two decimal places as needed.)=

Find the P-value for the found test statistic.

P-value (Round to four decimal places as needed.)=

State the conclusion. Choose the correct answer below.

A. Reject . There is sufficient evidence to support the claim that fewer than half of all

teenagers in the population feel that grades are the greatest source of pressure.

B. Do not reject . There is sufficient evidence to support the claim that fewer than half of all

teenagers in the population feel that grades are the greatest source of pressure.

C. Reject . There is insufficient evidence to support the claim that fewer than half of all

teenagers in the population feel that grades are the greatest source of pressure.

D. Do not reject . There is insufficient evidence to support the claim that fewer than half of

all teenagers in the population feel that grades are the greatest source of pressure.

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