Hypothesis Practice 1

8/13/2019 Hypothesis Practice 1

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Hypothesis Testing Handout 1: Hypotheses, Tails, Errors

Name___________________________________

MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.A hypothesis test is to be performed. Determine the null and alternative hypotheses.

1) In the past, the mean running time for a certain type of flashlight battery has been 9.0 hours. The

manufacturer has introduced a change in the production method and wants to perform ahypothesis test to determine whether the mean running time has changed as a result.

A) H0

: µ =9.0 hours

Ha

: µ ≠ 9.0 hours

B) H0

: µ ≥ 9.0 hours

Ha

: µ =9.0 hours

C) H0

: µ ≠ 9.0 hours

Ha

: µ =9.0 hours

D) H0

: µ =9.0 hours

Ha

: µ >9.0 hours

1)

2) The maximum acceptable level of a certain toxic chemical in vegetables has been set at 0.6 parts

per million (ppm). A consumer health group measured the level of the chemical in a randomsample of tomatoes obtained from one producer to determine whether the mean level of the

chemical in these tomatoes exceeds the recommended limit.A) H

0 : µ = 0.6 ppm

Ha

: µ > 0.6 ppm

B) H0

: µ > 0.6 ppm

Ha

: µ = 0.6 ppm

C) H0

: µ < 0.6 ppm

Ha

: µ > 0.6 ppm

D) H0

: µ = 0.6 ppm

Ha

: µ ≥ 0.6 ppm

2)

3) A manufacturer claims that the mean amount of juice in its 16 ounce bottles is 16.1 ounces. A

consumer advocacy group wants to perform a hypothesis test to determine whether the meanamount is actually less than this.

A) H0

: µ = 16.1 ounces

H a : µ <

16.1

ounces

B) H0

: µ < 16.1 ounces

H a : µ =

16.1

ouncesC) H

0 : µ > 16.1 ounces

Ha

: µ < 16.1 ounces

D) H0

: µ = 16.1 ounces

Ha

: µ ≤ 16.1 ounces

3)

Classify the hypothesis test as two tailed, left tailed, or right tailed.4) The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. A

hypothesis test is to be performed to decide whether adult women are, on average, getting lessthan the RDA of 75 milligrams per day.

A) Two-tailed B) Left-tailed C) Right-tailed

4)

5) The mean credit card debt among households in one state is $8400. A hypothesis test is to beperformed to decide whether the mean credit card debt for households in the formerly affluenttown of Rich-No-More differs from the mean credit card debt for the state.

A) Two-tailed B) Left-tailed C) Right-tailed

5)

1



6) A psychologist has designed a test to measure stress levels in adults. She has determined thatnationwide the mean score on her test is 27. A hypothesis test is to be conducted to determine

whether the mean score for trial lawyers exceeds the national mean score.A) Two-tailed B) Left-tailed C) Right-tailed

6)

For the given hypothesis test, explain the meaning of a Type I error, a Type II error, or a correct decision as specified.7) At one school, in 2005, the average amount of time that tenth-graders spent watching television

each week was 21.6 hours. The principal introduced a campaign to encourage the students towatch less television. One year later, in 2006, the principal performed a hypothesis test todetermine whether the average amount of time spent watching television per week haddecreased. The hypotheses are:

H0

: µ = 21.6 hours

Ha

: µ < 21.6 hours

where µ is the mean amount of time, in 2006, that tenth-graders spend watching television each

week

Explain the meaning of a correct decision.A) A correct decision would occur if, in fact, µ = 21.6 hours, and the results of the sampling

lead to rejection of the null hypothesis; or if, in fact, µ < 21.6 hours and the results of the

sampling lead to that conclusion.B) A correct decision would occur if, in fact, µ = 21.6 hours, and the results of the sampling do

not lead to rejection of that fact; or if, in fact, µ < 21.6 hours and the results of the sampling

do not lead to rejection of the null hypothesis that µ = 21.6 hours.

C) A correct decision would occur if, in fact, µ = 21.6 hours, and the results of the sampling do

not lead to rejection of that fact; or if, in fact, µ < 21.6 hours and the results of the sampling

lead to that conclusion.D) A correct decision would occur if, in fact, µ < 21.6 hours and the results of the sampling do

not lead to rejection of the null hypothesis that µ = 21.6 hours.

7)


consumer advocacy group wants to perform a hypothesis test to determine whether the meanamount is actually less than this. The hypotheses are:

H0

: µ = 16.1 ounces

Ha

: µ < 16.1 ounces

where µ is the mean amount of juice in the manufacturer's 16 ounce bottles. Explain the meaning

of a Type I error.A) A Type I error would occur if, in fact, µ < 16.1 ounces, but the results of the sampling fail to

lead to that conclusion.B) A Type I error would occur if, in fact, µ = 16.1 ounces, but the results of the sampling lead

to the conclusion that µ < 16.1 ounces.

C) A Type I error would occur if, in fact, µ < 16.1 ounces, but the results of the sampling lead

to the conclusion that µ > 16.1 ounces.

D) A Type I error would occur if, in fact, µ = 16.1 ounces, but the results of the sampling do

not lead to rejection of that fact.

8)

2



9) A health insurer has determined that the "reasonable and customary" fee for a certain medicalprocedure is $1200. They suspect that the mean fee charged by one particular clinic for thisprocedure is higher than $1200. The insurer wants to perform a hypothesis test to determinewhether their suspicion is correct. The hypotheses are:

H0

: µ = $1200

Ha

: µ > $1200

where µ is the mean amount charged by the clinic for this procedure. Explain the meaning of a

correct decision.A) A correct decision would occur if, in fact, µ = $1200, and the results of the sampling lead to

rejection of the null hypothesis; or if, in fact, µ > $1200 and the results of the sampling lead

to that conclusion.B) A correct decision would occur if, in fact, µ > $1200 and the results of the sampling do not

lead to rejection of the null hypothesis that µ = $1200.

C) A correct decision would occur if, in fact, µ = $1200, and the results of the sampling do not

lead to rejection of that fact; or if, in fact, µ > $1200 and the results of the sampling lead to

that conclusion.D) A correct decision would occur if, in fact, µ = $1200, and the results of the sampling do not

lead to rejection of that fact; or if, in fact, µ > $1200 and the results of the sampling do not

lead to rejection of the null hypothesis that µ = $1200.

9)

10) In 2000, the mean math SAT score for students at one school was 485. Five years later, in 2005, a

teacher performed a hypothesis test to determine whether the average math SAT score of students at the school had changed from the 2000 mean of 485. The hypotheses were:

H0

: µ =485

Ha

: µ ≠ 485

where µ is the mean math SAT score, in 2005, for students at the school

Explain the meaning of a Type I error.A) A Type I error would occur if, in fact, µ ≠ 485, and the results of the sampling lead to that

conclusion.

B) A Type I error would occur if, in fact, µ =485, but the results of the sampling lead to the

conclusion that µ ≠ 485

C) A Type I error would occur if, in fact, µ ≠ 485, but the results of the sampling fail to lead to

that conclusion.D) A Type I error would occur if, in fact, µ =485, but the results of the sampling do not lead to

rejection of that fact

10)

3



11) A man is on trial accused of murder in the first degree. The prosecutor presents evidence that hehopes will convince the jury to reject the hypothesis that the man is innocent. This situation can

be modeled as a hypothesis test with the following hypotheses:

H0

: The defendant is innocent.

Ha

: The defendant is guilty.

Explain the meaning of a Type II error.A) A Type II error would occur if, in fact, the defendant is guilty and the jury rejects the null

hypothesis that he is innocent.B) A Type II error would occur if, in fact, the defendant is innocent but the jury concludes

that he is guilty.C) A Type II error would occur if, in fact, the defendant is guilty but the jury fails to conclude

that he is guilty.D) A Type II error would occur if, in fact, the defendant is innocent and the jury fails to reject

the null hypothesis that he is innocent.

11)

12) In 2000, the mean math SAT score for students at one school was 487. Five years later, in 2005, a

teacher performed a hypothesis test to determine whether the average math SAT score of students at the school had changed from the 2000 mean of 487. The hypotheses were:

H 0 : µ =487H

a : µ ≠ 487

where µ is the mean math SAT score, in 2005, for students at the school

Explain the meaning of a Type II error.A) A Type II error would occur if, in fact, µ =487, but the results of the sampling do not lead

to rejection of that factB) A Type II error would occur if, in fact, µ ≠ 487, and the results of the sampling lead to that

conclusion.C) A Type II error would occur if, in fact, µ =487, but the results of the sampling lead to the

conclusion that µ ≠ 487

D) A Type II error would occur if, in fact, µ ≠ 487, but the results of the sampling fail to lead

to that conclusion.

12)


per million (ppm). A consumer health group measured the level of the chemical in a randomsample of tomatoes obtained from one producer to determine whether the mean level of thechemical in these tomatoes exceeds the recommended limit.

The hypotheses are

H0

: µ = 0.4 ppm

Ha

: µ > 0.4 ppm

where µ is the mean level of the chemical in tomatoes from this producer. Explain the meaning of a Type I error.

A) A Type I error would occur if, in fact, µ = 0.4 ppm, but the results of the sampling fail tolead to rejection of that fact.

B) A Type I error would occur if, in fact, µ > 0.4 ppm, and the results of the sampling lead to

rejection of the null hypothesis that µ = 0.4 ppm.

C) A Type I error would occur if, in fact, µ = 0.4 ppm, but the results of the sampling lead to

the conclusion that µ > 0.4 ppm

D) A Type I error would occur if, in fact, µ > 0.4 ppm, but the results of the sampling fail to

lead to that conclusion.

13)

4



14) The recommended dietary allowance (RDA) of vitamin C for women is 75 milligrams per day. Ahypothesis test is to be performed to decide whether adult women are, on average, getting lessthan the RDA of 75 milligrams per day. The hypotheses are

H0

: µ = 75 mg

Ha

: µ < 75 mg

where µ

is

the

mean

vitamin

C

intake

(per

day)

of

all

adult

females.

Explain

the

meaning

of

aType II error.

A) A Type II error would occur if, in fact, µ = 75 mg, and the results of the sampling do not

lead to rejection of that fact.B) A Type II error would occur if, in fact, µ < 75 mg, and the results of the sampling lead to

rejection of the null hypothesis that µ = 75 mg.

C) A Type II error would occur if, in fact, µ = 75 mg, but the results of the sampling lead to

the conclusion that µ < 75 mg

D) A Type II error would occur if, in fact, µ < 75 mg, but the results of the sampling fail to

lead to that conclusion.

14)

15) A psychologist has designed a test to measure stress levels in adults. She has determined thatnationwide the mean score on her test is 20. A hypothesis test is to be conducted to determine

whether the mean score for trial lawyers exceeds the national mean score. The hypotheses are

H0

: µ =20

Ha

: µ >20

where µ is the mean score for all trial lawyers. Explain the meaning of a Type I error.A) A Type I error would occur if, in fact, µ >20, but the results of the sampling fail to lead to

that conclusion.B) A Type I error would occur if, in fact, µ =20, but the results of the sampling fail to lead to

rejection of that fact.C) A Type I error would occur if, in fact, µ =20, but the results of the sampling lead to the

conclusion that µ > 20.

D) A Type I error would occur if, in fact, µ >20, but the results of the sampling lead to

rejection of the null hypothesis that µ =20.

15)

Classify the conclusion of the hypothesis test as a Type I error, a Type II error, or a correct decision.16) In the past, the mean running time for a certain type of flashlight battery has been 9.9 hours. The

manufacturer has introduced a change in the production method and wants to perform ahypothesis test to determine whether the mean running time has increased as a result. Thehypotheses are:

H0

: µ =9.9 hours

H a :

µ >

9.9

hourswhere µ is the mean running time of the new batteries

Suppose that the results of the sampling lead to nonrejection of the null hypothesis. Classify thatconclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean runningtime has increased.

A) Type I error B) Type II error C) Correct decision

16)

5



17) In the past, the mean running time for a certain type of flashlight battery has been 8.1 hours. The

manufacturer has introduced a change in the production method and wants to perform ahypothesis test to determine whether the mean running time has increased as a result. Thehypotheses are:

H0

: µ =8.1 hours

Ha

: µ >8.1 hours

where µ is the mean running time of the new batteries

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify thatconclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean runningtime has not increased.

A) Correct decision B) Type I error C) Type II error

17)


consumer advocacy group wants to perform a hypothesis test to determine whether the meanamount is actually less than this. The hypotheses are:

H0

: µ = 16.1 ounces

Ha

: µ < 16.1 ounces

where µ is the mean amount of juice in the manufacturer's 16 ounce bottles.

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify thatconclusion as a Type I error, a Type II error, or a correct decision, if in fact the mean amount of

juice, µ , is less than 16.1 ounces.

A) Type I error B) Correct decision C) Type II error

18)

19) A health insurer has determined that the "reasonable and customary" fee for a certain medicalprocedure is $1200. They suspect that the average fee charged by one particular clinic for thisprocedure is higher than $1200. The insurer wants to perform a hypothesis test to determinewhether their suspicion is correct. The hypotheses are:

H0

: µ = $1200

H

a

: µ > $1200

where µ is the mean amount charged by the clinic for this procedure.

Suppose that the results of the sampling lead to rejection of the null hypothesis. Classify thatconclusion as a Type I error, a Type II error, or a correct decision, if in fact the average feecharged by the clinic is $1200 .


19)


per million (ppm). A consumer health group measured the level of the chemical in a randomsample of tomatoes obtained from one producer to determine whether the mean level of thechemical in these tomatoes exceeds the recommended limit.

The hypotheses are

H0

: µ = 0.7 ppm

Ha

: µ > 0.7 ppm

where µ is the mean level of the chemical in tomatoes from this producer. Suppose that theresults of the sampling lead to nonrejection of the null hypothesis. Classify that conclusion as aType I error, a Type II error, or a correct decision, if in fact the mean level of the chemical in thesetomatoes is greater than 0.7 ppm.


20)

6



Answer KeyTestname: HYPOTHESIS PRACTICE 1

1) A2) A3) A4) B

5) A6) C7) C8) B9) C

10) B11) C12) D13) C14) D15) C16) B17) B18) B19) B20) C

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Hypothesis Practice 1