Question 1

Which is not a type of comparison for which you would anticipate a two-sample test?

Accepted Answer

Two-sample tests are used to compare two groups or samples. Option C involves comparing a sample mean with a desired mean, which does not involve two groups or samples. Therefore, it is not a type of comparison for which you would anticipate a two-sample test.

Question 2

A medical researcher compared the variances in birth weights for five randomly chosen babies of each gender, with the MegaStat results shown below. F-test for equality of variance
$ \quad $$3.537$ $ \quad $variance: Boys
$ \quad $$3.288$$ \quad $ variance: Girls
$ \quad $$1.08 $$ \quad $ F
$ \quad $$.9453 $$ \quad $p-value The population variances:

Accepted Answer

The F-test for equality of variance resulted in a p-value of .9453, indicating that there is no significant difference in the variances between the two populations. Therefore, it is reasonable to assume that the variances are equal at any customary level of significance (α).

Question 3

The table below shows two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations. $$\begin{array} { l r r } 
\text { Statistic } & \text { Ann Arbor } & \text { Livonia } \
\text { Mean } & 25.817 & 31.248 \
\text { St Dev } & 3.389 & 1.874 \
\text { Sample size } & 7 & 10
\end{array}$$ What are the critical values for a two-tailed test for equal variances at ? = .05?

Accepted Answer

The answer of The table below shows two samples taken...

Question 4

The coach of an adult Master's Swim class selected eight swimmers within each of the two age groups shown below. A 50-yard freestyle time is recorded for each swimmer. The resulting times (seconds) are shown below. Which statistical test would you choose to compare the two groups? $$\begin{array} { c c c } 
&  { \text { Age Group } } \
\text { Obs } & 25 - 34 \text { Yrs } & 35 - 44 \text { Yrs } \
1 & 26.26 & 31.08 \
2 & 28.44 & 28.63 \
3 & 26.61 & 25.65 \
4 & 29.74 & 31.81 \
5 & 26.94 & 27.22 \
6 & 26.31 & 30.56 \
7 & 34.68 & 33.38 \
8 & 22.55 & 30.82 \
& & \
\text { Mean } & 27.69 & 29.89 \
\text { St Dev } & 3.50 & 2.54
\end{array}$$

Accepted Answer

Since the variances of the two groups are not known and they are independent, we should use the t-test for independent samples with unknown variances.

Question 5

The table below shows two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations. $$\begin{array} { l r r } 
\text { Statistic } & \text { Ann Arbor } & \text { Livonia } \
\text { Mean } & 25.817 & 31.248 \
\text { St Dev } & 4.389 & 1.874 \
\text { Sample size } & 7 & 10
\end{array}$$ At ? = .05, can you conclude that the first sample has a larger variance than the second sample?

Accepted Answer

The answer of The table below shows two samples taken...

Question 6

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

The p-value of .4407 is greater than any customary alpha level (e.g., 0.05, 0.01), indicating that there is not enough evidence to reject the null hypothesis that the population means are equal.

Question 7

Jason wants to perform a two-tailed test for equality between two independent sample proportions. Each sample has at least 10 "successes" and 10 "failures." Jason's test statistic is -1.44. What is his p-value?

Accepted Answer

The p-value is the probability of getting a test statistic as extreme as or more extreme than the one observed, assuming the null hypothesis is true. In this case, the test statistic is -1.44, which is a z-score. The p-value for a two-tailed test with a z-score of -1.44 is 0.1498.

Question 8

Random samples of students were compared to see whether or not there was a difference in the proportion favoring the university's proposed switch from MWF (three-day) classes to MW and TR (two-day) classes. The results shown below are from MegaStat. Analyze these results thoroughly.
Hypothesis test for two independent proportions
$\begin{array} { r r r l l } \text { Residents } & \text { Commuters } & p _ { c } & \ 0.400 & 0.600 & 0.500 & \mathrm { p } \text { (as decimal) } \ 80 / 200 & 120 / 200 & 200 / 400 & \mathrm { p } \text { (as fraction) } \ 80 . & 120 . & 200 & \mathrm { X } \ 200 & 200 & 400 & \mathrm { n } \end{array}$

$- 0.200$$ \quad $ difference
$0.000$ $ \quad $ hypothesized difference
$0.050$ $ \quad $ std. error
$- 4.000 $$ \quad $ z
$.0001$ $ \quad $p-value (two-tailed)

Accepted Answer

The answer of Random samples of students were compared to...

Question 9

Group 1 has a mean of 13.4 and group 2 has a mean of 15.2. Both populations are known to have a variance of 9.0 and each sample consists of 18 items. What is the test statistic to test for equality of population means?

Accepted Answer

The answer of Group 1 has a mean of 13.4...

Question 10

The table below compares two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations. Very briefly, what conclusions can you draw?

Accepted Answer

The answer of The table below compares two samples taken...

Question 11

Does the Speedo Fastskin II Male Hi-Neck Bodyskin competition racing swimsuit improve a swimmer's 200-yard individual medley performance times? A test of 100 randomly chosen male varsity swimmers at several different universities showed that 66 enjoyed improved times, compared with only 54 of 100 female varsity swimmers. In comparing the proportions of males versus females, is it safe to assume normality?

Accepted Answer

The answer of Does the Speedo Fastskin II Male Hi-Neck...

Question 12

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 13

Does the Speedo Fastskin II Male Hi-Neck Bodyskin competition racing swimsuit improve a swimmer's 200-yard individual medley performance times? A test of 100 randomly chosen male varsity swimmers at several different universities showed that 66 enjoyed improved times, compared with only 54 of 100 female varsity swimmers. To test for equality in the proportions of men versus women who experienced improvement, the test statistic is approximately:

Accepted Answer

The test statistic is calculated using the formula for comparing two proportions. The result, approximately 1.73, does not depend on the tail of the test (one-tailed or two-tailed) for its calculation, only for its interpretation against a critical value.

Quiz 10: Two-Sample Hypothesis Tests

Which is not a type of comparison for which you would anticipate a two-sample test?

Jason wants to perform a two-tailed test for equality between two independent sample proportions. Each sample has at least 10 "successes" and 10 "failures." Jason's test statistic is -1.44. What is his p-value?

Group 1 has a mean of 13.4 and group 2 has a mean of 15.2. Both populations are known to have a variance of 9.0 and each sample consists of 18 items. What is the test statistic to test for equality of population means?

The table below compares two samples taken to compare the mean age of individuals who purchased the iPhone 3G at two AT&T store locations. Very briefly, what conclusions can you draw?