Exercise 1:

An engineer is going to redesign an ejection seat for an airplane. The seat was designed for pilots weighing between 130 lb and 171 lb. The new population of pilots has normally distributed weights with a mean of 138 lb and a standard deviation of 34.8 lb.

a. If a pilot is randomly selected, find the probability that his weight is between 130 lb and 171 lb.

The probability is approximately________.

(Round to four decimal places as needed.)

b. If 37 different pilots are randomly selected, find the probability that their mean weight is between 130 lb and 171 lb.

The probability is approximately________.

(Round to four decimal places as needed.)

c. When redesigning the ejection seat, which probability is more relevant?

A. Part (b) because the seat performance for a sample of pilots is more important.

B. Part (b) because the seat performance for a single pilot is more important.

C. Part (a) because the seat performance for a single pilot is more important.

D. Part (a) because the seat performance for a sample of pilots is more important.

Exercise 2:

Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 80 mm Hg. Use a significance level of 0.05.

Right Arm103102947574

Left Arm177170146143144

The regression equation isy = ____+_____x. (Round to one decimal place as needed.)

Given that the systolic blood pressure in the right arm is 80 mm Hg, the best predicted systolic blood pressure in the left arm is _______mm Hg.

(Round to one decimal place as needed.)

Exercise 3:

Find the regression equation, letting the first variable be the predictor (x) variable. Using the listed lemon/crash data, where lemon imports are in metric tons and the fatality rates are per 100,000 people, find the best predicted crash fatality rate for a year in which there are 450 metric tons of lemon imports. Is the prediction worthwhile?

Lemon Imports231268350461550

Crash Fatality Rate15.915.615.215.315

Find the equation of the regression line.

y =_______+_______x(Round the constant three decimal places as needed. Round the coefficient to six decimal places as needed.)

The best predicted crash fatality rate for a year in which there are 450 metric tons of lemon imports is ______fatalities per 100,000 population.

(Round to one decimal place as needed.)

Is the prediction worthwhile?

A. Since the sample size is small, the prediction is not appropriate.

B. Since common sense suggests there should not be much of a relationshipbetween the two variables, the prediction does not make much sense.

C. Since all of the requirements for finding the equation of the regression line are met, the prediction is worthwhile.

D. Since there appears to be an outlier, the prediction is not appropriate.

Exercise 4:

A poll was conducted to investigate opinions about global warming. The respondents who answered yes when asked if there is solid evidence that the earth is getting warmer were then asked to select a cause of global warming. The results are given in the accompanying data table. Use a 0.05 significance level to test the claim that the sex of the respondent is independent of the choice for the cause of global warming. Do men and women appear to agree, or is there a substantial difference?

Human activityNatural patternsDon't know

Male30914359

Female29816160

Identify the null and alternative hypotheses.

Ho: (1)__________and (2)___________are (3)_____________

H1: (4)__________and (5)___________are (6)_____________

Compute the test statistic.

_________________________

(Round to three decimal places as needed.)

Find the critical value(s).

____________________

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

What is the conclusion based on the hypothesis test?

(7)_____________ Ho. There (8)___________sufficient evidence to warrant rejection of the claim that the sex of the respondent is independent of the choice for the cause of global warming. Men and women (9)__________to agree.

(1) Respondents who answered yes

The choice for human activity

The sex of the respondent

(2) the choice for the cause of global warming

the respondents who answered no

the choice for natural patterns

(3) independent.

dependent.

(4) Respondents who answered yes

The choice for human activity

The sex of the respondent

(5) the respondents who answered no

the choice for natural patterns

the choice for the cause of global warming

(6) independent.

dependent.

(7) Reject

Fail to reject

(8) is not

is

(9) do not appear

appear

Exercise 5:

Samples of pages were randomly selected from three different novels. The Flesch Reading Ease scores were obtained from each page, and the TI-83/84 Plus calculator results from analysis of variance are given below. Use a 0.05 significance level to test the claim that the three books have the same mean Flesch Reading Ease score.

What is the conclusion for this hypothesis test?

A. Reject Ho. There is sufficient evidence to warrant rejection of the claim that thethree books have the same mean Flesch Reading Ease score.

B. Fail to reject Ho. There is insufficient evidence to warrant the rejection of theclaim that the three books have the same mean Flesch Reading Ease score.

C. Reject Ho. There is insufficient evidence to warrant the rejection of the claim that the three books have the same mean Flesch Reading Ease score.

D. Fail to reject Ho. There is sufficient evidence to warrant the rejection of theclaim that the three books have the same mean Flesch Reading Ease score.

________________________________________________________

3: Calculator results

One-way ANOVA

F = 9.8039492028

p = 4.7746426E4

Factor

df = 2

SS = 1436.00895

MS = 718.004477

One-way ANOVA

MS = 718.004477

Error

df = 32

SS = 2343.56001

MS =73.2362502

Sxp = 8.55781807

________________________________________________________

Exercise 6:

An investigator analyzed the leading digits from 787 checks issued by seven suspect companies. The frequencies were found to be 4, 11, 2, 72, 371, 281, 7, 16, and 23, and those digits correspond to the leading digits of 1, 2, 3, 4, 5, 6, 7, 8, and 9, respectively. If the observed frequencies are substantially different from the frequencies expected with Benford's law shown below, the check amounts appear to result from fraud. Use a 0.025 significance level to test for goodness-of-fit with Benford's law. Does it appear that the checks are the result of fraud?

Leading Digit:123456789

Actual Frequency:41127237128171623

Benford's Law:30.1%17.6%12.5%9.7%7.9% 6.7%5.8% 5.1%4.6%

Determine the null and alternative hypotheses.

Ho: (1)_________________H1: (2)_________________

Calculate the test statistic, 2.

2 = _______________

(Round to three decimal places as needed.)

Calculate the P-value.

P-value = _______________

(Round to four decimal places as needed.)

State the conclusion.

(3)_________________Ho. There (4)______________sufficient evidence to warrant rejection of the claim that the leading digits are from a population with a distribution that conforms to Benford's law. It (5)________________that the checks are the result of fraud.

Choose from the following options:

(1) a.At least two leading digits have frequencies that do not conform to Benford'slaw.

b.The leading digits are from a population that conforms to Benford's law.

c.At most three leading digits have frequencies that do not conform to Benford'slaw.

d.At least one leading digit has a frequency that does not conform to Benford's law.

(2) a. The leading digits are from a population that conforms to Benford's law.

b. At most three leading digits have frequencies that do not conform to Benford'slaw.

c. At least one leading digit has a frequency that does not conform to Benford'slaw.

d. At least two leading digits have frequencies that do not conform to Benford'slaw.

(3) Do not reject

Reject

(4) is

is not

(5) does appear

does not appear

Exercise 7:

The table below includes results from polygraph (lie detector) experiments conducted by researchers. In each case, it was known if the subjected lied or did not lie, so the table indicates when the polygraph test was correct. Use a 0.05 significance level to test the claim that whether a subject lies is independent of the polygraph test indication. Do the results suggest that polygraphs are effective in distinguishing between truth and lies?

Determine the null and alternative hypotheses.

A. Ho: Polygraph testing is not accurate.

H1: Polygraph testing is accurate.

B. Ho: Whether a subject lies is independent of the polygraph test indication.

H1: Whether a subject lies is not independent of the polygraph test indication.

C. Ho: Polygraph testing is accurate.

H1: Polygraph testing is not accurate.

D. Ho: Whether a subject lies is not independent of the polygraph test indication.

H1: Whether a subject lies is independent of the polygraph test indication.

Determine the test statistic.

2 = ____________

(Round to three decimal places as needed.)

Determine the P-value of the test statistic.

P-value = ____________

(Round to four decimal places as needed.)

Do the results suggest that polygraphs are effective in distinguishing between truth and lies?

A. There is not sufficient evidence to warrant rejection of the claim that whether asubject lies is independent of the polygraph test indication.

B. There is sufficient evidence to warrant rejection of the claim that whether asubject lies is independent of the polygraph test indication.

C. There is not sufficient evidence to warrant rejection of the claim that polygraphtesting is 95% accurate.

D. There is sufficient evidence to warrant rejection of the claim that polygraphtesting is 95% accurate.

___________________________________________________________________________

Did the Subject Actually Lie?

No (Did Not Lie)Yes (Lied)

Polygraph test indicated that the subject lied.2041

Polygraph test indicated that the subject did not lie.2211

_____________________________________________________

Exercise 8:

Use the technology display, which results from the head injury measurements from car crash dummies listed below. The measurements are in hic (head injury criterion) units, and they are from the same cars used for the table below. Use a 0.10 significance level to test the given claim.

Test the null hypothesis that head injury measurements are not affected by an interaction between the type of car (foreign, domestic) and size of the car (small, medium, large). What do you conclude?

What are the null and alternative hypotheses?

A.Ho: Head injury measurements are not affected by an interaction between type of carand size of the car.

H1: Head injury measurements are affected by an interaction between type ofcar and size of the car.

B.Ho: Head injury measurements are affected by an interaction between type of carand size of the car.

H1: Head injury measurements are not affected by an interaction between type ofcar and size of the car.

C.Ho: Head injury measurements are not affected by type of car.

H1: Head injury measurements are affected by type of car.

D.Ho: Head injury measurements are not affected by size of car.

H1: Head injury measurements are affected by size of car.

Find the test statistic.

F = _____________

(Round to two decimal places as needed.)

Determine the P-value.

P-value = __________

(Round to three decimal places as needed.)

Determine whether there is sufficient evidence to support the given alternative hypothesis.

Since the P-value is (1)___________0.10, (2)__________Ho. There is (3)_______evidence to support the alternative hypothesis. Conclude that there (4)________appear to be an effect from an interaction between the type of car (foreign or domestic) and whether the car is small, medium, or large.

_____________________________________________________

5: Data Table

Size of Car

SmallMediumLarge

Foreign291250340

548501696

507396333

Domestic408472217

374368331

370345168

_____________________________________________________

_____________________________________________________

SourceDFSSMSFP

Type13636036360.12.420.146

Size2143967198.20.480.630

Interaction24122120610.71.370.290

Error1218011315009.4

Total17272091

_____________________________________________________

Find the correct answer below:

(1) less than or equal to

greater than

(2) reject

fail to reject

(3) sufficient

insufficient

(4) does not

does

Exercise 9:

A sample of colored candies was obtained to determine the weights of different colors. The ANOVA table is shown below. It is known that the population distributions are approximately normal and the variances do not differ greatly. Use a 0.05 significance level to test the claim that the mean weight of different colored candies is the same. If the candy maker wants the different color populations to have the same mean weight, do these results suggest that the company has a problem requiring corrective action?

Source:DF:SS:MS:Test Stat, F:Critical F:P-Value:

Treatment:60.0120.0020.65422.19660.6866

Error:940.2820.003

Total:1000.294

Should the null hypothesis that all the colors have the same mean weight be rejected?

A.Yes, because the P-value is greater than the significance level.

B. No, because the P-value is greater than the significance level.

C.Yes, because the P-value is less than the significance level.

D. No, because the P-value is less than the significance level.

Does the company have a problem requiring corrective action?

A. No, because it is likely that the candies do not have equal mean weights.

B.Yes, because it is not likely that the candies do not have equal mean weights.

C. No, because it is not likely that the candies do not have equal mean weights.

D. Yes, because it is likely that the candies do not have equal mean weights.

Exercise 10:

Listed below are amounts of bills for dinner and the amounts of the tips that were left. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of = 0.01. If everyone were to tip with the same percentage, what should be the value of r?

Bill (dollars)31.6252.2090.3699.4260.70100.52

Tip (dollars)3.9010.408.6218.1310.6012.95

Construct a scatterplot.Click below.

Scatterplot Needed for Question10 of Final Exam

The linear correlation coefficient r is ________.

(Round to three decimal places as needed.)

Determine the null and alternative hypotheses.

Ho: (1)____________________________

H1: (2)___________________________

(Type integers or decimals. Do not round.)

The test statistic is _________.

(Round to two decimal places as needed.)

The P-value is _________.

(Round to three decimal places as needed.)

Because the P-value of the linear correlation coefficient is (3) ___________the significance level, there (4)____________sufficient evidence to support the claim that there is a linear correlation between bill amounts and tip amounts.

If everyone were to tip with the same percentage, then r = ________ .

(Round to three decimal places as needed.)

(1)

>

=

<

(2) >

=

<

(3) greater than

less than or equal to

(4) is not

is

Exercise 11:

Researchers conducted an experiment to test the effects of alcohol. Errors were recorded in a test of visual and motor skills for a treatment group of 21 people who drank ethanol and another group of 21 people given a placebo. The errors for the treatment group have a standard deviation of 2.40, and the errors for the placebo group have a standard deviation of 0.83. Use a 0.05 significance level to test the claim that the treatment group has errors that vary significantly more than the errors of the placebo group. Assume that the two populations are normally distributed.

What are the null and alternative hypotheses?

A. Ho:12

22

H1:12

=22

B. Ho:12

=22

H1:12

>22

C. Ho:12

=22

H1:12

<22

D. Ho:12

=22

H1:12

22

Identify the test statistic.

________________

(Round to two decimal places as needed.)

Use technology to identify the P-value.

______________

(Round to three decimal places as needed.)

What is the conclusion for this hypothesis test?

A.Fail to reject Ho. There is sufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

B.Reject Ho. There is insufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

C.Reject Ho. There is sufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

D.Fail to reject Ho. There is insufficient evidence to support the claim that the treatment group has errors that vary significantly more than the errors of the placebo group.

Exercise 12

A study was done on proctored and nonproctored tests. The results are shown in the table. Assume that the two samples are independent simple random samples selected from normally distributed populations, and do not assume that the population standard deviations are equal. Complete parts (a) and (b) below. Use a significance level 0.01 for both parts.

___________________________________________________________________

ProctoredNonproctored

12

n3432

x

74.8683.25

s10.5118.27

_______________________________________________

a) Test the claim that students taking nonproctored tests get a higher mean score than those taking proctored tests.

What are the null and alternative hypotheses?

A.Ho: 1 = 2

H1: 1 < 2

B.Ho: 1 = 2

H1: 1 2

C.Ho: 1 = 2

H1: 1 > 2

D.Ho: 1 2

H1: 1 < 2

The test statistic, t, is____________.

(Round to two decimal places as needed.)

The P-value is_________.

(Round to three decimal places as needed.)

State the conclusion for the test.

A. Fail to reject Ho. There is sufficient evidence to support the claim that studentstaking nonproctored tests get a higher mean score than those taking proctored tests.

B. Reject Ho. There is not sufficient evidence to support the claim that students taking

nonproctored tests get a higher mean score than those taking proctored tests.

C.Reject Ho. There is sufficient evidence to support the claim that students taking

nonproctored tests get a higher mean score than those taking proctored tests.

D.Fail to reject Ho. There is not sufficient evidence to support the claim that studentstaking nonproctored tests get a higher mean score than those taking proctored tests.

b) Construct a confidence interval suitable for testing the claim that students takingnonproctored tests get a higher mean score than those taking proctored tests.

________< 1 2 <________

(Round to two decimal places as needed.)

Does the confidence interval support the conclusion of the test?

(1) ________ because the confidence interval contains (2) ________

1) Yes,

No,

(2) only negative values.

zero.

only positive values.

Exercise 13:

A simple random sample of front-seat occupants involved in car crashes is obtained. Among2946occupants not wearing seat belts,31were killed. Among7602occupants wearing seat belts,16were killed. Use a0.01significance level to test the claim that seat belts are effective in reducing fatalities. Complete parts (a) through (c) below.

a.Test the claim using a hypothesis test.

Consider the first sample to be the sample of occupants not wearing seat belts and the second sample to be the sample of occupants wearing seat belts. What are the null and alternative hypotheses for the hypothesis test?

A.H0: p1 p2

H1: p1 p2

B.H0: p1 p2

H1: p1 = p2

C.H0: p1 p2

H1: p1 p2

D.H0: p1 = p2

H1: p1 > p2

E.H0: p1 = p2

H1: p1 < p2

F.H0: p1 = p2

H1: p1 p2

Identify the test statistic.

z = _________

(Round to two decimal places as needed.)

Identify the P-value.

P-value =_________

(Round to three decimal places as needed.)

What is the conclusion based on the hypothesis test

The P-value is (1)_________the significance level of = 0.01, so (2)_________the null hypothesis. There (3)_________sufficient evidence to support the claim that the fatality rate is higher for those not wearing seat belts.

b. Test the claim by constructing an appropriate confidence interval.

The appropriate confidence interval is_________< p1 p2 <_________.

(Round to three decimal places as needed.)

What is the conclusion based on the confidence interval?

Because the confidence interval limits (4)_________0, it appears that the two fatality rates are (5)_________.

Because the confidence interval limits include (6) __________ values, it appears that the fatality rate is (7)_________for those not wearing seat belts.

c) What do the results suggest about the effectiveness of seat belts?

A. The results suggest that the use of seat belts is associated with the same fatality ratesas not using seat belts.

B. The results suggest that the use of seat belts is associated with lower fatality ratesthan not using seat belts.

C. The results suggest that the use of seat belts is associated with higher fatality ratesthan not using seat belts.

D. The results are inconclusive.

(1) less than

greater than

(2) reject

fail to reject

(3) is not

is

(4) include

do not include

(5) not equal.

equal.

(6) only positive

positive and negative

only negative

(7) lower

higher

the same

Exercise 14:

Conduct the hypothesis test and provide the test statistic and the critical value, and state the conclusion.

A person drilled a hole in a die and filled it with a lead weight, then proceeded to roll it200times. Here are the observed frequencies for the outcomes of 1, 2, 3, 4, 5, and 6, respectively:28, 27, 40, 38, 26, 41.Use a0.01significance level to test the claim that the outcomes are not equally likely. Does it appear that the loaded die behaves differently than a fair die?

The test statistic is __________.

(Round to three decimal places as needed.)

The critical value is__________.

(Round to three decimal places as needed.)

State the conclusion.

(1)__________ Ho. There (2)__________sufficient evidence to support the claim that the outcomes are not equally likely. The outcomes (3)__________to be equally likely, so the loaded die (4)__________to behave differently from a fair die.

(1) Do not reject

Reject

(2) is

is not

(3) appear

do not appear

(4) does not appear

appears