Deck 8: Testing the Difference Between Two Means, Two Proportions, and Two Variances

Question 1

A) 3.00
B) 4.28
C) 12.85
D) 2.00

Answer 1

C

Question 2

Answer 2

B

Question 3

Answer 3

False

Question 4

When finding the F -test value, the smaller of the variances is placed in the numerator.

Question 5

Samples are independent when they are not related.

Question 6

When subjects are matched according to one variable, the matching process does not eliminate the
influence of other variables.

Question 7

One of the requirements for the z - test for comparing two proportions is that the samples must be
dependent on each other.

Question 8

Calculate the critical value. Use Refer To: 09-18

A) -1.65
B) -2.33
C) -2.58
D) -1.96

Question 9

A) 7.85
B) 0.33
C) 0.39
D) 2.58

Question 10

The critical value for a two-tailed F -test is 2.65, when , the sample size from which the variance
for the numerator was obtained = 10, and the sample size from which the variance for the denominator
was obtained = 15.

Question 11

If the samples are dependent, the f - test for dependent samples is used.

Question 12

Question 13

The critical value for a one-tailed right F -test is 2.57, when , the degrees of freedom for the
numerator = 15, and the degrees of freedom for the denominator = 20.

Question 14

If the test value in the figure below, for a test of the difference between two large sample means, is 2.57 when the critical value is 1.96, what decision about the hypothesis should be made?

A) reject the null hypothesis
B) accept the null hypothesis
C) reject the alternative hypothesis
D) not enough information

Question 15

For normally distributed populations, if two samples are independent and the variances are known, the z -
test is used.

Question 16

When hypothesizing a difference of 0, if the confidence interval does not contain 0, the null hypothesis is
rejected.

Question 17

What is the test value? Use Refer To: 09-18

A) -6.86
B) -3.70
C) -4.13
D) -5.45

Question 18

The value of F cannot be negative, because variances are always positive or zero.

Question 19

When comparing two variances or standard deviations, a f -test is used.

Question 20

The standard error of difference of two large (independent) sample means is

Question 21

A researcher hypothesizes that the variation in the amount of money spent on business dinners is greater than the amount of money spent on lunches. The variance of nine business dinners was $6.12, and the
Variance of 12 business lunches was $0.87. What is the test value?

A) 3.1
B) 9.61
C) 49.5
D) 7.03

Question 22

Question 23

A) Yes, because the test value -8.45 is outside the interval (-1.96, 1.96)
B) Yes, because the test value -2.86 is outside the interval (-1.96, 1.96)
C) Yes, because the test value 71.43 is outside the interval (-1.96, 1.96)
D) No, because the test value -0.03 is inside the interval (-1.96, 1.96)

Question 24

A) -2.36
B) -0.22
C) -0.55
D) -4.38

Question 25

If the variances are not known, and one or both sample sizes are less than 30, the F -test must be
used.

Question 26

What is the critical value for a two-tailed F -test with when the sample size from which the variance for the numerator was obtained was 10, and the sample size from which the denominator was
Obtained was 24?

A) 2.27
B) 2.25
C) 2.32
D) 2.30

Question 27

A) The data do not support the claim because the test value 0.94 is less than 1.64.
B) The data do not support the claim because the test value 0.94 is less than 1.96.
C) The data support the claim because the test value 1.94 is less than 1.96.
D) The data support the claim because the test value 1.94 is greater than 1.65.

Question 28

A) Fail to reject the hypothesis because the test value 3.00 is less than the critical value 3.01.
B) Reject the hypothesis because the test value 3.00 is less than the critical value 3.01.
C) Fail to reject the hypothesis because the test value 9.00 is greater than the critical value 2.88.
D) Reject the hypothesis because the test value 9.00 is greater than the critical value 2.88.

Question 29

A researcher hypothesizes that the variation in the car rental rates at a major citiy's airport is less than the car rental rates in that city. The variance of 7 airport car rental rates was $25 and the variance of 4 city car
Rental rates was $60. What is the test value?

A) 4.20
B) 1.55
C) 2.40
D) 5.76

Question 30

Compute the critical value for a right-tailed F -test with

A) 2.12
B) 2.23
C) 2.20
D) 2.16

Question 31

What is the critical value? Use (Use the variances unequal formula.)

A) -1.761
B) -2.045
C) -1.697
D) -1.703

Question 32

A) 0.01
B) 0.025
C) 0.05
D) 0.1

Question 33

A) test value = 0.45, degrees of freedom = 19 and 29
B) test value = 0.45, degrees of freedom = 18 and 28
C) test value = 2.20, degrees of freedom = 28 and 18
D) test value = 2.20, degrees of freedom = 29 and 19

Question 34

Question 35

A) No, because the test value 0.26 is inside the interval (-1.96, 1.96)
B) Yes, because the test value 3.81 is outside the interval (-1.96, 1.96)
C) Yes, because the test value 1.33 is inside the interval (-1.96, 1.96)
D) No, because the test value 1.33 is outside the interval (-1.96, 1.96)

Question 36

A) The data do not support the claim because the test value 0.48 is less than 1.28.
B) The data do not support the claim because the test value 0.98 is less than 1.28.
C) The data do not support the claim because the test value 0.98 is less than 1.64.
D) The data do not support the claim because the test value 0.48 is less than 1.64.

Question 37

A car salesman claims that the variance of prices on convertibles is higher than the variance on station wagons. The standard deviation of 16 convertibles is $6,800 and the standard deviation of 24 station
Wagons is $3,900. For what is the test value?

A) 3.00
B) 3.04
C) 2.78
D) 2.33

Question 38

What is the test value? Use . (Use the variances unequal formula.)

A) -6.97
B) -2.50
C) -4.53
D) -2.54

Question 39

A college class believes that the average grade averages of psychology students and the average grade averages of biology students are different. The class found that the actual grade averages of a sample of
10 psychology students was 3.2, and the average grade average of a sample of 10 biology students was

Question 40

A) 3.31
B) 1.75
C) 0.31
D) 2.31

Question 41

For the samples summarized below, test the hypothesis at $\ddagger=.05$ that the two variances are equal. $$\begin{array} { | l | c | c | } \hline & \text { Variance } & \text { Number of data values } \\\hline \text { Sample 1 } & 29 & 9 \\\hline \text { Sample } 2 & 10 & 19 \\\hline\end{array}$$

A) Accept the hypothesis because the test value 8.41 is greater than the critical value 3.01.
B) Reject the hypothesis because the test value 2.90 is less than the critical value 2.88.
C) Reject the hypothesis because the test value 8.41 is greater than the critical value 2.88.
D) Accept the hypothesis because the test value 2.90 is less than the critical value 3.01.

Question 42

When testing the difference between two proportions, one sample had 30 out of 100 who were for capital punishment, and the other sample had 60 out of 80 who were for capital punishment. Calculate the
Standard error.

A) 0.075
B) 0.060
C) 0.042
D) 0.098

Question 43

Many elementary school students in a school district currently have ear infections. A random sample of children in two different schools found that 13 of 46 at one school and 15 of 30 at the other had this
Infection. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists
Between the proportion of students who have ear infections at one school and the other?
AYes, there is sufficient information to reject the hypothesis that the proportions of students at the two
) schools who have ear infections are the same because the test value -16.96 is outside the acceptance
Region (-1.96,1.96).
BNo, there is not sufficient information to reject the hypothesis that the proportions of students at the two
) schools who have ear infections are the same because the test value -1.92 is inside the acceptance region
(-1)96,1.96).
CYes, there is sufficient information to reject the hypothesis that the proportions of students at the two
) schools who have ear infections are the same because the test value -2.52 is outside the acceptance
Region (-1.96,1.96).
DYes, there is sufficient information to reject the hypothesis that the proportions of students at the two
) schools who have ear infections are the same because the test value -9.44 is outside the acceptance
Region (-1.96,1.96).

Question 44

70% of students at a university live on campus. A random sample found that 35 of 50 male students and 42 of 50 of female students lived on campus. At the .05 level of significance, is there sufficient evidence
To conclude that a difference exists between the proportion of male students who live on campus and the
Proportion of female students who live on campus?
ANo, there is not sufficient information to reject the hypothesis that the proportion of male students who
) live on campus and the proportion of female students who live on campus are the same because the test
Value -0.14 is inside the acceptance region (-1.96,1.96).
BNo, there is not sufficient information to reject the hypothesis that the proportion of male students who
) live on campus and the proportion of female students who live on campus are the same because the test
Value -0.90 is inside the acceptance region (-1.96,1.96).
CNo, there is not sufficient information to reject the hypothesis that the proportion of male students who
) live on campus and the proportion of female students who live on campus are the same because the test
Value -1.73 is inside the acceptance region (-1.96,1.96).
DNo, there is not sufficient information to reject the hypothesis that the proportion of male students who
) live on campus and the proportion of female students who live on campus are the same because the test
Value -1.66 is inside the acceptance region (-1.96,1.96).

Question 45

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.

State the alternative hypothesis.

Question 46

In comparing the two standard deviations below, what is the test value and what are the degrees of freedom that should be used?

A) test value = 3.50, degrees of freedom = 17 and 25
B) test value = 3.50, degrees of freedom = 16 and 24
C) test value = 12.25, degrees of freedom = 17 and 25
D) test value = 12.25, degrees of freedom = 16 and 24

Question 47

A reporter bought a hamburger at each of a set of random stores of two different restaurant chains. She then had the number of calories in each hamburger measured. Can the reporter conclude, at $\ddagger=.05,$ that the two sets of hamburgers have different amounts of calories? (Use the equal variances formula.)
$$\begin{array} { | l | c | c | } \hline & \text { Women } & \text { Men } \\\hline \text { Sample size } & 7 & 8 \\\hline \text { Mean spending amount } & 80 & 95 \\\hline \text { Sample variance } & 400 & 800 \\\hline\end{array}$$

A) No, because the test value -0.09 is inside the interval (-2.14, 2.14)
B) No, because the test value -0.09 is inside the interval (-2.16, 2.16)
C) No, because the test value -1.17 is inside the interval (-2.16, 2.16)
D) No, because the test value -2.00 is inside the interval (-2.16, 2.16)

Question 48

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.

What is the critical value using ?

A) -1.782
B) -1.761
C) -1.943
D) -1.895

Question 49

A marketing firm asked a random set of married women and married men how much they were willing to spend for jewellery as a present for their spouse. Can the firm conclude, at , that
Each of the two groups has a different willingness to spend? (Use the unequal variances formula.)

A) No, because the test value 0.32 is inside the interval (-2.31, 2.31)
B) Yes, because the test value 2.81 is outside the interval (-2.36, 2.36)
C) Yes, because the test value 16.00 is inside the interval (-2.31, 2.31)
D) No, because the test value 16.00 is outside the interval (-2.36, 2.36)

Question 50

One poll found that 40% of male voters will support a candidate while another found that 48% of female voters will be in support. To test whether this candidate has equal levels of support between male and
Female voters, the alternative hypothesis should be

Question 51

A study of cats and dogs found that 25 of 50 cats and 44 of 60 dogs slept more than 10 hours per day. At the .05 level of significance, is there sufficient evidence to conclude that a difference exists between the
Proportion of cats and the proportion of dogs that sleep more than 10 hours per day?
AYes, there is sufficient information to reject the hypothesis that the proportion of cats and the proportion
) of dogs that sleep more than 10 hours per day are the same because the test value -2.52 is outside the
Acceptance region (-1.96,1.96).
BNo, there is not sufficient information to reject the hypothesis that the proportion of cats and the
) proportion of dogs that sleep more than 10 hours per day are the same because the test value -1.64 is
Inside the acceptance region (-1.96,1.96).
CYes, there is sufficient information to reject the hypothesis that the proportion of cats and the proportion
) of dogs that sleep more than 10 hours per day are the same because the test value -2.90 is outside the
Acceptance region (-1.96,1.96).
DNo, there is not sufficient information to reject the hypothesis that the proportion of cats and the
) proportion of dogs that sleep more than 10 hours per day are the same because the test value -0.77 is
Inside the acceptance region (-1.96,1.96).

Question 52

A recent survey reported that in a sample of 300 students who attend community colleges, 105 work at least 20 hours a week. In a sample of 225 students attending universities, only 20 students were found to
Work at least 20 hours per week. What is the test value?

A) 6.95
B) 7.61
C) 2.38
D) 4.18

Question 53

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.

A running coach wanted to see whether runners ran faster after eating spaghetti the night before a race. Twenty-four random runners were chosen for this study. They ran a 5-kilometre race after having a
Normal dinner the night before, and then a week later, re-ran the same race after having a spaghetti dinner
The night before. Their results (in seconds) are in the table below. At , what is the test value for
This test?

A) -3.41
B) -1.00
C) -0.26
D) -4.90

Question 54

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.

Determine the mean of the difference.

A) -0.96
B) -6.3
C) 1.43
D) -1.43

Question 55

A) 5.78
B) 8.43
C) 71.14
D) 17.97

Question 56

One poll found that 41% of male voters will support a candidate while another found that 49% of female voters will be in support. To test whether this candidate has equal levels of support between male and
Female voters, the null hypothesis should be

Question 57

A medical researcher is interested in whether patients' left arms or right arms are longer. If 9 patients participate in this study (so that 9 left arms and 9 right arms are measured), how many degrees of freedom
Should the researcher use in her t-test critical value?

A) 8
B) 9
C) 16
D) 17

Question 58

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.

Compute the standard deviation of the difference.

A) 0.78
B) 0.69
C) 0.87
D) 0.48

Question 59

A) 2.25
B) 2.42
C) 2.64
D) 2.88

Question 60

A researcher wanted to determine if using an octane booster would increase gasoline mileage. A random
sample of seven cars was selected; the cars were driven for two weeks without the booster and two weeks
with the booster.

A dietician investigated whether apples turned brown at different rates when exposed to air after being washed in hot water or in cold water. She took 12 random apples and cut each in half. She washed one
Half of each apple in hot water and the other half in cold water, and then put both halves out in a tray. Her
Results (in hours until turning a particular shade of brown) are in the table below. At , did she see a
Difference between the two treatments?

A) No, because the test value -0.06 is inside the range (-3.05, 3.05).
B) No, because the test value -0.21 is inside the range (-3.11, 3.11).
C) No, because the test value -0.21 is inside the range (-3.05, 3.05).
D) No, because the test value -0.06 is inside the range (-3.11, 3.11).

Question 61

Question 62

A pooled estimate of the variance is a weighted average of the variance using the two sample variances
and the __________ of each variance as the weights.
________________________________________

Question 63

A study on the oxygen consumption rate (OCR) of sea cucumbers involved a random sample of size 10 at 15oC and a second random sample of size 7 kept at 18oC. If one tested the hypothesis that this range
Of temperature had no effect on the OCR, the degrees of freedom for the test statistic would be (assume
Equal variability)

A) 9
B) 10
C) 15
D) 16

Question 64

________________________________________

Question 65

The mean value of F is approximately equal to __________.
________________________________________

Question 66

Question 67

When the subjects are paired or matched in some way, samples are considered to be __________.
________________________________________

Question 68

A study on the oxygen consumption rate (OCR) of sea cucumbers involved a random sample of size 10 at 15oC and second random sample of size 7 kept at 18oC. If one tested the hypothesis that this range of
Temperature had no effect on the OCR (assume equal variability) the critical value would be (assume .05)

A) 1.746
B) 1.761
C) 2.131
D) 2.145

Question 69

Question 70

Question 71

Question 72

The critical value for a left-tailed t-test for dependent samples is __________ when the degrees of
freedom = 7 and

Question 73

In a study comparing the systolic blood pressure of individuals sitting and standing, 10 subjects had their blood pressure measured in the two conditions. The investigator planned to test the hypothesis that the
Mean blood pressure readings are the same sitting and standing (the subjects remained in each position
For 5 minutes). If the investigator tests at the 10% level of significance, the rejection region would be

Question 74