Deck 10: Two-Sample Confidence Intervals

Question 1

A sample of students is enrolled in an online statistics class, and another sample is enrolled in a traditional statistics class. At the end of the semester, the students are given a test. The scores from
Each sample are compared to determine which class was more effective. Are these samples
Independent or paired?

A) Independent
B) Paired

Answer 1

Independent

Question 2

A sample of students is enrolled in a speed-reading class. Each takes a reading test before and after the class. The two samples of scores are compared to determine how large an improvement in
Reading speed occurred. Are these samples independent or paired?

A) Independent
B) Paired

Answer 2

Paired

Question 3

A survey of college students reported that in a sample of 442 male students, the average number of energy drinks consumed per month was 1.82 with a standard deviation of 4.84, and in a sample of
80 female students, the average was 1.89 with a standard deviation of 3.26.
Construct a 98% confidence interval for the difference between men and women in the mean number
Of energy drinks consumed. Based on your results, is it reasonable to believe that the mean number
Of energy drinks consumed may be the same for both male and female students?

A) No
B) Yes

Answer 3

Yes

Question 4

A survey of college students reported that in a sample of 371 male students, the average number of energy drinks consumed per month was 2.47 with a standard deviation of 4.70, and in a sample of
282 female students, the average was 1.45 with a standard deviation of 3.12.
Construct a 98% confidence interval for the difference between men and women in the mean number
Of energy drinks consumed.

A) (-5.40, 7.44)
B) (0.21, 1.83)
C) (0.26, 1.78)
D) (0.31, 1.73)

Question 5

In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A, and 10 randomly
Selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured
From each plot. Following are the results. Assume that the populations are approximately normal. Construct a 95% confidence interval for the
Difference between the mean yields for the two types of fertilizer.

A) (20.3, 64.6)
B) (16.4, 68.6)
C) (14.0, 70.9)
D) (19.0, 65.9)

Question 6

The following MINITAB output display presents a 95% confidence interval for the difference between two means.

A) 26
B) 13.847
C) 28
D) 35.992

Question 7

The concentration of hexane (a common solvent) was measured in units of micrograms per liter for a simple random sample of twelve specimens of untreated ground water taken near a municipal
Landfill. The sample mean was 720.2 with a sample standard deviation of 8.8. Eleven specimens of
Treated ground water had an average hexane concentration of 695.1 with a standard deviation of 9.1.
It is reasonable to assume that both samples come from populations that are approximately normal. Construct
A 90% confidence interval for the reduction of hexane concentration after treatment.

A) (23.6, 26.6)
B) (18.3, 31.9)
C) (21.8, 28.4)
D) (22.2, 28.0)

Question 8

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the difference between two means. The sample sizes are

A) 123.288
B) 40.864
C) 42.032
D) -1.557

Question 9

Using technology, solve the following problem: An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for
Driving the golf ball down range.) She hits fourteen balls with driver A and 10 balls with driver B. The drive
Distances (in yards) for the trials are show below. Assume that the populations are approximately normal. Construct a 95% confidence interval for the
Difference between the mean drive distances for the two drivers.

A) (-31.88, 17.22)
B) (-37.24, 22.58)
C) (1,016.33, 296.53)
D) (1,386.82, 509.86)

Question 10

An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls
With driver A and 10 balls with driver B. The drive distances (in yards) for the trials are show below. Assume that the populations are approximately normal. Construct a 90% confidence interval for the
Difference between the mean drive distances for the two drivers.

A) (-13.5, 24.1)
B) (-12.6, 23.2)
C) (-9.9, 20.5)
D) (-11.0, 21.6)

Question 11

In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land were treated with fertilizer A, and 10 randomly
Selected plots were treated with fertilizer B. The number of pounds of harvested fruit was measured
From each plot. Following are the results. Assume that the populations are approximately normal. Construct a 95% confidence interval for the
Difference between the mean yields for the two types of fertilizer. Based on your results, is it
Reasonable to conclude that the mean yields may be the same for fertilizers A and B?

A) Yes
B) No

Question 12

Using technology, solve the following problem: In an agricultural experiment, the effects of two fertilizers on the production of oranges were measured. Fourteen randomly selected plots of land
Were treated with fertilizer A, and 10 randomly selected plots were treated with fertilizer B. The
Number of pounds of harvested fruit was measured from each plot. Following are the results. Assume that the populations are approximately normal. Construct a 98% confidence interval for the
Difference between the mean yields for the two types of fertilizer.

A) (80.766, 6,763.582)
B) (8.987, 82.241)
C) (19.740, 7,531.810)
D) (4.443, 86.786)

Question 13

How many degrees of freedom did the calculator use?

A) -0.439
B) -41.874
C) 19.678187
D) 80.827

Question 14

An amateur golfer wishes to determine if there is a difference between the drive distances of her two favorite drivers. (A driver is a specialized club for driving the golf ball down range.) She hits fourteen balls
With driver A and 10 balls with driver B. The drive distances (in yards) for the trials are show below. Assume that the populations are approximately normal. Construct a 98% confidence interval for the
Difference between the mean drive distances for the two drivers. Based on your results, is it
Reasonable to conclude that the mean drive distances may be the same for drivers A and B?

A) Yes
B) No

Question 15

The following MINITAB output display presents a 95% confidence interval for the difference between two means.

A) -34.409
B) 89.948
C) 13
D) -48.804

Question 16

Using technology, solve the following problem: The concentration of hexane (a common solvent) was measured in units of micrograms per liter for a simple random sample of fourteen specimens of
Untreated ground water taken near a municipal landfill. The sample mean was 241.8 with a sample
Standard deviation of 8.8. Ten specimens of treated ground water had an average hexane
Concentration of 149.5 with a standard deviation of 7.4.
It is reasonable to assume that both samples come from populations that are approximately normal. Construct
A 95% confidence interval for the reduction of hexane concentration after treatment.

A) (9.242, 9.960)
B) (85.407, 99.193)
C) (86.595, 98.005)
D) (9.306, 9.900)

Question 17

Fill in the blanks: We are 95% confident that the difference between the means is between _________ and _________.

A) 22.420, 26.525
B) 110.794, 160.497
C) 0, 13.038055
D) -71.757, -27.649

Question 18

Using technology, solve the following problem: A survey of college students reported that in a sample of 442 male students, the average number of energy drinks consumed per month was 2.39
With a standard deviation of 4.92, and in a sample of 77 female students, the average was 1.53 with
A standard deviation of 3.07.
Construct a 90% confidence interval for the difference between men and women in the mean number
Of energy drinks consumed.

A) (-5.5932, 7.3132)
B) (0.0707, 1.6493)
C) (0.1122, 1.6078)
D) (0.1676, 1.5524)

Question 19

A) (2.869, 0.666)
B) (-0.444, 7.444)
C) (-1.271, 8.271)
D) (-1.232, 8.231)

Question 20

A) (9.0, 15.8)
B) (10.3, 14.5)
C) (7.2, 17.6)
D) (10.8, 14.0)

Question 21

Traffic engineers compared rates of traffic collisions at intersections with raised medians and rates at intersections with two-way left-turn lanes. They found that out of 4,653 collisions at intersections
With raised medians, 2,289 were rear-end collisions, and out of 4,606 collisions at two-way left-turn
Lanes, 2,027 were rear-end collisions.
Assuming these to be random samples of collisions from the two types of intersections, construct a 95%
Confidence interval for the difference between the proportions of collisions that are of the rear-end
Type at the two types of intersection.

A) (0.032, 0.072)
B) (0.042, 0.061)
C) (0.472, 0.512)
D) (0.492, 0.440)

Question 22

Traffic engineers compared rates of traffic collisions at intersections with raised medians and rates at intersections with two-way left-turn lanes. They found that out of 4,512 collisions at intersections
With raised medians, 2,202 were rear-end collisions, and out of 4,277 collisions at two-way left-turn
Lanes, 1,903 were rear-end collisions.
Assuming these to be random samples of collisions from the two types of intersections, construct a 95%
Confidence interval for the difference between the proportions of collisions that are of the rear-end
Type at the two types of intersection. Does the confidence interval contradict the claim that the
Proportion of rear-end collisions is the same at both types of intersection?

A) No
B) Yes

Question 23

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the mean difference between matched pairs. How many degrees of freedom are there?

A) 16
B) 6.8168
C) 17
D) 2.4052

Question 24

In a random sample of 70 patients undergoing a standard surgical procedure, 16 required medication for postoperative pain. In a random sample of 85 patients undergoing a new procedure, only 17
Required medication.
Construct a 98% confidence interval for the difference in the proportions of patients needing pain
Medication between the old and new procedures. A physician claims that the proportion of patients
Who need pain medication is the same for both procedures. Does the confidence interval contradict
The claim?

A) No
B) Yes

Question 25

Two microprocessors are compared on a sample of 6 benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are given below: An electronics engineer claims that the mean speed is the same for both processors. Does
The 99% confidence interval contradict this claim? (Hint: First find the 99% confidence interval for
The difference between the mean speeds.)

A) No
B) Yes

Question 26

Two microprocessors are compared on a sample of 6 benchmark codes to determine whether there is a difference in speed. The times (in seconds) used by each processor on each code are given below: Find the 95% confidence interval for the difference between the mean speeds.

A) (-3.61, 8.14)
B) (-3.92, 8.45)
C) (-2.98, 7.51)
D) (-3.19, 7.72)

Question 27

A group of six individuals with high cholesterol levels were given a new diet designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after the
Implementation of the diet for each individual, with the following results: Find the 98% confidence interval for the mean reduction in cholesterol level.

A) (15.23, 59.77)
B) (17.85, 58.83)
C) (16.17, 15.23)
D) (18.79, 56.21)

Question 28

A group of six individuals with high blood pressure volunteered to test whether petting cats for 10 minutes can alter systolic blood pressure levels. Systolic blood pressures (in millimeters of mercury,
Or mmHg) were measured for each subject before and after petting cats for 10 minutes, with the
Following results: A researcher claims that the mean reduction in systolic blood pressure is 14 mmHg. Does the 98%
Confidence interval contradict this claim? (Hint: you need to find the 98% confidence interval for
The mean reduction in systolic blood pressure.)

A) No
B) Yes

Question 29

A computer software magazine compares the rates of malware infection for computers protected by security software A with the rates of infection for computers protected by security software B.
They found that out of 787 computers with security software A, 72 became infected with some type of
Malware after 1000 hours of internet interaction. For security software B, 37 out of 834 computers
Became infected after 1000 hours of internet interaction.
Assuming these to be random samples of infection rates for the two security software packages, construct a
98% confidence interval for the difference between the proportions of infection for the two types of
Security software packages. Does the confidence interval contradict the claim that the proportion of
Infections is the same for the two types of security software?

A) Yes
B) No

Question 30

A) (-0.048, 0.310)
B) (-0.063, 0.325)
C) (-0.038, 0.300)
D) (-0.054, 0.316)

Question 31

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the mean difference between matched pairs. What is the point estimate of ?

A) 7.00973
B) 17
C) 2.4052
D) 6.8168

Question 32

The following MINITAB output display presents a 95% confidence interval for the difference between two proportions.

A) -0.123422
B) 0.215778
C) 0.108
D) 0.057

Question 33

The following MINITAB output display presents a 95% confidence interval for the difference between two means. Fill in the blanks: We are 95% confident that the difference in the means is between ______
And ______.

A) 9, 15
B) 144.384, 168.966
C) 0, 19
D) -44.197, -4.967

Question 34

A group of six individuals with high blood pressure volunteered to test whether petting cats for 10 minutes can alter systolic blood pressure levels. Systolic blood pressures (in millimeters of mercury,
Or mmHg) were measured for each subject before and after petting cats for 10 minutes, with the
Following results: Find the 99% confidence interval for the mean reduction in systolic blood pressure.

A) (-47.97, 40.97)
B) (-56.42, 49.42)
C) (-49.31, 46.75)
D) (-53.75, -56.42)

Question 35

In a random sample of 65 patients undergoing a standard surgical procedure, 12 required medication for postoperative pain. In a random sample of 90 patients undergoing a new procedure, only 14
Required medication.
Construct a 98% confidence interval for the difference in the proportions of patients needing pain
Medication between the old and new procedures.

A) (-0.003, 0.061)
B) (0.185, 0.156)
C) (0.042, 0.328)
D) (-0.114, 0.172)

Question 36

The following MINITAB output display presents a 95% confidence interval for the difference between two proportions. Fill in the blanks: We are 95% confident that the difference between the proportions is between ______ and
______.

A) 0, 0.040462
B) 0.18007, 0.220532
C) 526, 572
D) -0.014, 0.095

Question 37

A computer software magazine compares the rates of malware infection for computers protected by security software A with the rates of infection for computers protected by security software B.
They found that out of 794 computers with security software A, 24 became infected with some type of
Malware after 1000 hours of internet interaction. For security software B, 47 out of 522 computers
Became infected after 1000 hours of internet interaction.
Assuming these to be random samples of infection rates for the two security software packages, construct a
95% confidence interval for the difference between the proportions of infection for the two types of
Security software packages.

A) (-0.083, -0.037)
B) (-0.086, -0.034)
C) (-0.085, -0.035)
D) (-0.087, -0.033)

Question 38

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the difference between two proportions. Compute the point estimate of

A) -0.004832
B) 0.062
C) 1,851
D) 91

Question 39

A group of six individuals with high cholesterol levels were given a new diet designed to lower cholesterol levels. Cholesterol levels, in milligrams per deciliter, were measured before and after the
Implementation of the diet for each individual, with the following results: A dietician claims that the mean reduction in cholesterol level is 51 milligrams per deciliter. Does the
98% confidence interval contradict this claim? (Hint: you need to find the 98% confidence interval
For the mean reduction in cholesterol level.)

A) No
B) Yes

Question 40

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the difference between two proportions. Fill in the blanks: We are 95% confident that the difference between two proportions is between _______ and
_______.

A) -0.032, 0.028
B) 0, 1,455
C) 0.138399, 0.140669
D) 718, 737

Question 41

The following output from MINITAB presents a confidence interval for the mean difference between matched pairs.

A) 3.2282, 8.84
B) 0.724738, 2.8059
C) 0, 6.0341
D) 4.4797, 7.5885

Question 42

The following output from MINITAB presents a confidence interval for the mean difference between matched pairs.

A) 1.57675
B) 15
C) 4.9474
D) 6.3070

Question 43

The following output from MINITAB presents a confidence interval for the mean difference between matched pairs. How many degrees of freedom are there?

A) 13
B) 14
C) 1.9327
D) 7.2315

Question 44

The following display from a TI-84 Plus calculator presents a 95% confidence interval for the mean difference between matched pairs. Fill in the blanks: We are 95% confident that the mean difference is between ______ and ______.

A) 0, 10.2663
B) 6.714808, 13.817792
C) 2.6779, 17.8547
D) 0, 20