Question 1

A paired t-test with two columns of 8 observations in each column would use d.f. = 7.

Accepted Answer

A) True 
 B)False

Question 2

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 To compare the means, would it be appropriate to use a test that assumes equal variances?

Accepted Answer

A) Yes, because by pooling our variances, we can simplify our calculations. 
B) Yes, we should assume equal variances when comparing independent samples. 
C) No, because the sample statistics show that the variances are unequal at ? = .05. 
D) No, because the variances will differ because the means differ significantly. 
A) Yes, because by pooling our variances, we can simplify our calculations. 
B) Yes, we should assume equal variances when comparing independent samples. 
C) No, because the sample statistics show that the variances are unequal at ? = .05. 
D) No, because the variances will differ because the means differ significantly.

Question 3

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 comparing these two proportions, normality of the difference may be assumed because:

Accepted Answer

A) the populations are large enough to be assumed normal. 
B) the probability of success can reasonably be assumed constant. 
C) the samples are random, so the proportions are unbiased estimates. 
D) nπ ≥ 10 and n(1 - π) ≥ 10 for each sample taken separately. 
A) the populations are large enough to be assumed normal. 
B) the probability of success can reasonably be assumed constant. 
C) the samples are random, so the proportions are unbiased estimates. 
D) nπ ≥ 10 and n(1 - π) ≥ 10 for each sample taken separately.

Question 4

If the sample proportions were p1 = 12/50 and p2 = 18/50, the 95 percent confidence interval for the difference of the population proportions is approximately:

Accepted Answer

A) [-.144, +.244]. 
B) [-.120, +.120]. 
C) [-.298, +.058]. 
D) [-.011, +.214]. 
A) [-.144, +.244]. 
B) [-.120, +.120]. 
C) [-.298, +.058]. 
D) [-.011, +.214].

Question 5

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. She weighed a random sample of five babies of each gender. Their weights (pounds) are shown below, along with some MegaStat results. 
$\begin{array}{|r|r|r|}
\hline \text { Boys } & {\text { Girls }} \
\hline 5.920 & 5.740 &mean\
\hline 1.881 & 1.813&std. dev. \
\hline 5 & 5&n\
\hline
\end{array}$

$\begin{aligned}
8 & \text { df } \
0.1800 & \text { difference (Boys - Girls) } \
3.4125 & \text { pooled variance } \
1.8473 & \text { pooled std. dev. } \
1.1683 & \text { standard error of difference } \
0 & \text { hypothesized difference } \
0.15 & \text { t } \
.4407 & \text { p-value (one-tailed, upper) }
\end{aligned}$ The population means:

Accepted Answer

A) may be assumed equal at any customary ?. 
B) should be assumed unequal at any customary ?. 
C) are not relevant to this paired t-test. 
A) may be assumed equal at any customary ?. 
B) should be assumed unequal at any customary ?. 
C) are not relevant to this paired t-test.

Question 6

The F test is used to test for the equality of two population variances.

Accepted Answer

A) True 
 B)False

Question 7

In a test of a new surgical procedure, the five most respected surgeons in FlatBroke Township were invited to Carver Hospital. Each surgeon was assigned two patients of the same age, gender, and overall health. One patient was operated upon in the old way, and the other in the new way. Both procedures are considered equally safe. The surgery times are shown below: $ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$ \quad $$\text { Surgeon }$
$\begin{array} { |c | c | c | c | c | c | } 
\hline { \text { Allen } } & { \text { Bob } } & { \text { Chloe } } & \text { Daphne } &  { \text { Edgar } } \
\hline  \text { Old way } & 36 & 55 & 28 & 40 & 62 \
\hline \text { New way } & 31 & 45 & 28 & 35 & 57 \
\hline
\end{array}$ The time (in minutes) to complete each procedure was carefully recorded. In a right-tailed test for a difference of means, the test statistic is:

Accepted Answer

A) 3.162 
B) 1.645 
C) 1.860 
D) 2.132 
A) 3.162 
B) 1.645 
C) 1.860 
D) 2.132

Question 8

In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be:

Accepted Answer

A) -1.960 
B) -2.101 
C) -1.734 
D) -1.645 
A) -1.960 
B) -2.101 
C) -1.734 
D) -1.645

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 pooled proportion for this test is:

Accepted Answer

A) .130 
B) .140 
C) .145 
D) .146 
A) .130 
B) .140 
C) .145 
D) .146

Question 10

When testing the difference between two population proportions, it is necessary to use the same size sample from each population.

Accepted Answer

A) True 
 B)False

Question 11

John wants to compare two means. His sample statistics were $\bar { x } _ { 1 } = 22.7 , s _ { 1 } ^ { 2 } = 5.4 , n _ { 1 } = 9$ and $\bar { x } _ { 2 } = 20.5 , s _ { 2 } ^ { 2 } = 3.6 , n _ { 2 } = 9$ . Assuming equal variances, the test statistic is:

Accepted Answer

A) 2.37 
B) 2.20 
C) 1.96 
D) Must know ? to answer. 
A) 2.37 
B) 2.20 
C) 1.96 
D) Must know ? to answer.

Question 12

A new policy of "flex hours" is proposed. Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change. Management wonders if there is a difference between the two groups. What is the test statistic to test for a zero difference in the population proportions?

Accepted Answer

A) 1.321 
B) 1.287 
C) 1.200 
D) -1.255 
A) 1.321 
B) 1.287 
C) 1.200 
D) -1.255

Question 13

A random sample of Ersatz University students revealed that 16 females had a mean of $22.30 in their wallets with a standard deviation of $3.20, while 6 males had a mean of $17.30 with a standard deviation of $9.60. At α = .10, to test for equal variances in a two-tailed test, the critical values are:

Accepted Answer

A) 0.441 and 3.24 
B) 0.556 and 2.27 
C) 0.345 and 4.62 
D) 0.387 and 2.90 
A) 0.441 and 3.24 
B) 0.556 and 2.27 
C) 0.345 and 4.62 
D) 0.387 and 2.90

Question 14

In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 cases, while in Paymor Hospital such exams were given in 110 out of 200 cases. The pooled proportion is:

Accepted Answer

A) .50 
B) .40 
C) .30 
D) .20 
A) .50 
B) .40 
C) .30 
D) .20

Question 15

In comparing the means of two independent samples, if the test statistic indicates a significant difference at α = .05, it will also be significant at α = .10.

Accepted Answer

A) True 
 B)False

Question 16

The degrees of freedom for the t-test used to compare two population means (independent samples) with unknown variances (assumed equal) will be n1 + n2 - 2.

Accepted Answer

A) True 
 B)False

Question 17

A new policy of "flex hours" is proposed. Random sampling showed that 28 of 50 female workers favored the change, while 22 of 50 male workers favored the change. Management wonders if there is a difference between the two groups. For a test comparing the two proportions, the assumption of normality for the difference of proportions is:

Accepted Answer

A) clearly justified. 
B) clearly unjustified. 
C) a borderline call. 
A) clearly justified. 
B) clearly unjustified. 
C) a borderline call.

Question 18

A medical researcher wondered if there is a significant difference between the mean birth weight of boy and girl babies. Random samples of 5 babies' weights (pounds) for each gender showed the following: $$\begin{array} { l l l l l l } 
\text { Boys } & 8.0 & 4.7 & 7.3 & 6.2 & 3.4 \
\text { Girls } & 5.3 & 2.8 & 6.4 & 6.8 & 7.4
\end{array}$$ To test the researcher's hypothesis, we should use the:

Accepted Answer

A) paired (dependent) samples t-test. 
B) independent samples t-test. 
C) large-sample z-test. 
D) t-test for correlation. 
A) paired (dependent) samples t-test. 
B) independent samples t-test. 
C) large-sample z-test. 
D) t-test for correlation.

Question 19

In a test for equality of two proportions, the sample proportions were p1 = 12/50 and p2 = 18/50. The test statistic is approximately:

Accepted Answer

A) -1.44. 
B) -1.31. 
C) -1.67. 
D) Must know α to answer. 
A) -1.44. 
B) -1.31. 
C) -1.67. 
D) Must know α to answer.

Question 20

When using independent samples to test the difference between two population means, it is desirable but not necessary for the sample sizes to be the same.

Accepted Answer

A) True 
 B)False

A paired t-test with two columns of 8 observations in each column would use d.f. = 7.

If the sample proportions were p₁ = 12/50 and p₂ = 18/50, the 95 percent confidence interval for the difference of the population proportions is approximately:

The F test is used to test for the equality of two population variances.

In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n₁ = 8 and n₂ = 12. At α = .05, the critical value would be:

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 pooled proportion for this test is:

When testing the difference between two population proportions, it is necessary to use the same size sample from each population.

John wants to compare two means. His sample statistics were $\bar { x } _ { 1 } = 22.7 , s _ { 1 } ^ { 2 } = 5.4 , n _ { 1 } = 9$ and $\bar { x } _ { 2 } = 20.5 , s _ { 2 } ^ { 2 } = 3.6 , n _ { 2 } = 9$ . Assuming equal variances, the test statistic is:

In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 cases, while in Paymor Hospital such exams were given in 110 out of 200 cases. The pooled proportion is:

In comparing the means of two independent samples, if the test statistic indicates a significant difference at α = .05, it will also be significant at α = .10.

The degrees of freedom for the t-test used to compare two population means (independent samples) with unknown variances (assumed equal) will be n₁ + n₂ - 2.

In a test for equality of two proportions, the sample proportions were p₁ = 12/50 and p₂ = 18/50. The test statistic is approximately:

When using independent samples to test the difference between two population means, it is desirable but not necessary for the sample sizes to be the same.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

Exam 10: Two-Sample Hypothesis Tests

A paired t-test with two columns of 8 observations in each column would use d.f. = 7.

If the sample proportions were p1 = 12/50 and p2 = 18/50, the 95 percent confidence interval for the difference of the population proportions is approximately:

The F test is used to test for the equality of two population variances.

In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n1 = 8 and n2 = 12. At α = .05, the critical value would be:

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 pooled proportion for this test is:

When testing the difference between two population proportions, it is necessary to use the same size sample from each population.

In a random sample of patient records in Cutter Memorial Hospital, six-month postoperative exams were given in 90 out of 200 cases, while in Paymor Hospital such exams were given in 110 out of 200 cases. The pooled proportion is:

In comparing the means of two independent samples, if the test statistic indicates a significant difference at α = .05, it will also be significant at α = .10.

The degrees of freedom for the t-test used to compare two population means (independent samples) with unknown variances (assumed equal) will be n1 + n2 - 2.

In a test for equality of two proportions, the sample proportions were p1 = 12/50 and p2 = 18/50. The test statistic is approximately:

When using independent samples to test the difference between two population means, it is desirable but not necessary for the sample sizes to be the same.

Overview of Statistics

Data Collection

Describing Data Visually

Descriptive Statistics

Probability

Discrete Probability Distributions

Continuous Probability Distributions

Sampling Distributions and Estimation

One-Sample Hypothesis Tests

Analysis of Variance

Simple Regression

Multiple Regression

Time Series Analysis

Chi-Square Tests

Nonparametric Tests

Quality Management

Filters

If the sample proportions were p₁ = 12/50 and p₂ = 18/50, the 95 percent confidence interval for the difference of the population proportions is approximately:

In a left-tailed test comparing two means with variances unknown but assumed to be equal, the sample sizes were n₁ = 8 and n₂ = 12. At α = .05, the critical value would be:

The degrees of freedom for the t-test used to compare two population means (independent samples) with unknown variances (assumed equal) will be n₁ + n₂ - 2.

In a test for equality of two proportions, the sample proportions were p₁ = 12/50 and p₂ = 18/50. The test statistic is approximately: