Question 1

Two well-known aviation training schools are being compared using random samples of their graduates. It is found that 70 of 140 graduates of Fly-More Academy passed their FAA exams on the first try, compared with 104 of 260 graduates of Blue Yonder Institute. To compare the pass rates, the p-value for a right-tailed test is approximately:

Accepted Answer

A)  .054
B)  .027
C)  .155
D)  .013 B

Question 2

The critical value in an F test for equal variances is the ratio of the sample variances.

Accepted Answer

A) True 
 B)False  False

Question 3

The Welch-Satterthwaite t-test for two means has the same degrees of freedom as the pooled samples t-test for two means.

Accepted Answer

A) True 
 B)False  False

Question 4

In a right-tailed test comparing two proportions, the test statistic was zcalc = +1.81. The p-value is:

Accepted Answer

A)  .9649
B)  .0351
C)  .4649
D)  Must know n to answer.

Question 5

During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. Assuming equal variances, the pooled variance is:

Accepted Answer

A)  296.59
B)  225.00
C)  400.00
D)  522.16

Question 6

The F distribution is never negative and is always skewed right.

Accepted Answer

A) True 
 B)False

Question 7

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test of equal means (assume equal variances), the pooled variance is:

Accepted Answer

A)  14.76
B)  26.00
C)  24.75
D)  27.54

Question 8

During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 667 pounds per 1000 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 679 pounds per 1000 miles with a standard deviation of 15 pounds. At α = 0.05, in a left-tailed test, the critical value to compare the means (assuming equal variances) is:

Accepted Answer

A)  -2.508
B)  -2.074
C)  -1.321
D)  -1.717

Question 9

At Huge University, a sample of 200 business school seniors showed that 26 planned to pursue an MBA degree, compared with 120 of 800 arts and sciences seniors. We want to know if the proportion is higher in the arts and sciences group. The p-value for a left-tailed test is approximately:

Accepted Answer

A)  .38
B)  .48
C)  .24
D)  .51

Question 10

Of 200 youthful gamers (under 18) who tried the new Z-Box-Plus game, 160 rated it "excellent," compared with only 144 of 200 adult gamers (18 or over). The pooled proportion for a test to compare the two proportions would be:

Accepted Answer

A)  .76
B)  .72
C)  .77
D)  Must know α to answer.

Question 11

Randomly chosen MBA students were asked their opinions about the ideal number of children for a married couple. The sample data were entered into MegaStat, and the following results were produced. Hypothesis Test: Independent Groups (t-test, unequal variance)

$\begin{array}{rc}
\text { Men } & \text { Women } \
2.812 & 2.1538 \text { mean } \
1.2505 & 0.5547 \text { std. dev. } \
11 & 13 \text { sample size } \
& 13 \text { pooled df }
\end{array}$
$ 0.6582 $ $ \quad $$ \quad $difference (Men - Women)
$ 0.40722 $ $ \quad $$ \quad $standard error of difference
0$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $ hypothesized difference
$ 1.62 $$ \quad $$ \quad $$ \quad $$ \quad $t
$ 0.065 $$ \quad $$ \quad $$ \quad $$ \quad $P-value (one-tailed, upper)

F-test for equality of variance
1.56375 variance: Men
$ 0.307692 $ $ \quad $variance: Women
$ 5.08$$ \quad $F
$ 0.01 $$ \quad $P-value What conclusion can you draw from this analysis at ? = .05?

Accepted Answer

A)  Men want larger families on average than women.
B)  Women want larger families on average than men.
C)  This is insufficient evidence to suggest a difference in means.
D)  We could conclude that men want larger families if we used a two-tailed test.

Question 12

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. MegaStat's results for a two-tailed test are shown below. $$\begin{array} { | r r l | } 
\hline p 1 & p 2 & \
0.15 & 0.12 & \mathrm { p } \text { (as decimal) } \
120 / 800 & 144 / 1200 & \mathrm { p } \text { (as fraction) } \
120 . & 144 . & \mathrm { X } \
800 & 1200 & \mathrm { n } \
& & \
0.03 & \text { sample difference } & \
0.00 & \text { hypothesized difference } & \
0.01545 & \text { std. error } & \
\text { x.xx } & \text { z } & \
.0522 & \text { p-value (two-tailed) } & \
\hline
\end{array}$$ At ? = .05, the two-tailed test for a difference in proportions is:

Accepted Answer

A)  just barely significant.
B)  not quite significant.
C)  not feasible due to nonnormality.

Question 13

The folded F-test for equality of variances:

Accepted Answer

A)  is rarely used because of its complexity.
B)  requires looking up the critical value for α/2.
C)  puts the smaller variance in the numerator.
D)  requires looking up two critical values of F instead of one.

Question 14

During a test period, an experimental group of 10 vehicles using an 85 percent ethanol-gasoline mixture showed mean CO2 emissions of 240 pounds per 100 miles, with a standard deviation of 20 pounds. A control group of 14 vehicles using regular gasoline showed mean CO2 emissions of 252 pounds per 100 miles with a standard deviation of 15 pounds. A quick comparison of the sample variances suggests that the population variances are:

Accepted Answer

A)  probably equal.
B)  probably unequal.
C)  incomparable.

Question 15

Mary did an analysis of acute care variances in samples of occupancy rates at two community hospitals and obtained the following results: F-test for equality of variance
$\begin{aligned}
108.243 & \text { variance: group } 1 \
98.371 & \text { variance: group } 2 \
1.100 & \text { F } \
0.905 & \text { p-value }
\end{aligned}$ Can Mary conclude that the variances are unequal at ? = .05?

Accepted Answer

A)  No, there isn't enough evidence to believe the variances are unequal.
B)  Yes, the analysis shows that the variances are unequal.
C)  You can't tell without knowing the sample sizes.

Question 16

Assuming unequal variances in a t-test for a zero difference of two means, we would:

Accepted Answer

A)  sum the degrees of freedom for each sample.
B)  use the larger degrees of freedom for simplicity.
C)  use a complicated formula for the degrees of freedom.
D)  use a z-test to be conservative in the calculation.

Question 17

Random samples of Tuesday and Friday withdrawals from a college-campus ATM were compared to see whether or not there was a difference in the means. The results shown below are from MegaStat. Analyze these results thoroughly.
Hypothesis Test: Independent Groups (t-test, unequal variance)

$\begin{array}{|r|r|r|}
\hline Friday & Tuesday\
\hline 82.40 & 41.00 &mean\
\hline 75.35 & 35.53&std. dev. \
\hline 25 & 20 & n\
\hline
\end{array}$

$35 $$ \quad $$ \quad $$ \quad $df 
$41.400$ $ \quad $difference (Friday - Tuesday)
$17.035$ $ \quad $standard error of difference
0 $ \quad $$ \quad $$ \quad $hypothesized difference
$2.430 $$ \quad $$ \quad $t
$.0204$$ \quad $ p-value (two-tailed)

Accepted Answer

The answer of Random samples of Tuesday and Friday withdrawals...

Question 18

In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 prostatectomy patients, while in Paymor Hospital such exams were given in 110 out of 200 cases. In a left-tailed test for equality of proportions, the p-value is:

Accepted Answer

A)  .9772
B)  .0228
C)  .4772
D)  .0517

Question 19

Carver Memorial Hospital's surgeons have a new procedure that they think will decrease the time to perform an appendectomy. A sample of 8 appendectomies using the old method had a mean of 38 minutes with a variance of 36 minutes, while a sample of 10 appendectomies using the experimental method had a mean of 29 minutes with a variance of 16 minutes. For a right-tailed test for equal means (assume equal variances), the critical value at α = .10 is:

Accepted Answer

A)  1.746
B)  1.337
C)  2.120
D)  2.754

Question 20

Management of Melodic Kortholt Company compared absenteeism rates in two plants on the third Monday in November. Of Plant A's 800 employees, 120 were absent. Of Plant B's 1200 employees, 144 were absent. MegaStat's results for a two-tailed test are shown below. $$\begin{array} { | r r l | } 
\hline p 1 & p 2 & \
0.15 & 0.12 & \mathrm { p } \text { (as decimal) } \
120 / 800 & 144 / 1200 & \mathrm { p } \text { (as fraction) } \
120 . & 144 . & \mathrm { X } \
800 & 1200 & \mathrm { n } \
& & \
0.03 & \text { sample difference } & \
0.00 & \text { hypothesized difference } & \
0.01545 & \text { std. error } & \
\text { x.xx } & \text { z } & \
.0522 & \text { p-value (two-tailed) } & \
\hline
\end{array}$$ The test statistic (shown as z = x.xx) is approximately:

Accepted Answer

A)  2.022
B)  1.960
C)  1.942
D)  1.645

Exam 10: Two-Sample Hypothesis Tests