Question 1

When we have two data sets that reveal 95% confidence intervals that differ from a hypothesized value and don't overlap, what conclusion can we make?

Accepted Answer

A)  Although these groups differ from the hypothesized value, they don't differ from one another. 
B)  These groups are not significantly different from one another. 
C)  These groups are significantly different from one another. 
D)  We lack good evidence to decide whether these groups are significantly different from one another or not.

Question 2

If the mean of population A is significantly different from 20, but the mean of group B is not significantly different from 20, then the mean of the two population are different from one another.

Accepted Answer

A) True 
 B)False

Question 3

Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the difference in the mean population density values?
?
Number of fish caught in six seines before and after drainage connection.

$\begin{array}{lll}
\underline {\text {Vial  } }&\underline {\text { Before } }&\underline {\text {  After } }\
1 & 24 & 20 \
2 & 35 & 31 \
3 & 64 & 59 \
4 & 51 & 52 \
5 & 25 & 28 \
6 & 48 & 39
\end{array}$

Accepted Answer

A)  -1.0 
B)  -2.0 
C)  -3.0 
D)  -4.0

Question 4

Draw a flowchart to describe the steps you would take when presented with data from two different groups, and the goal is to identify if the means of the groups differ. You may assume the data values are normally distributed. Include each possible statistical test.

Accepted Answer

The answer of Draw a flowchart to describe the steps...

Question 5

Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows:
Near (group 1): mean = 6.1, SD = 0.35, n = 12
Far (group 2): mean = 5.8, SD = 0.30, n = 9
What is the standard error of the difference between the two means?

Accepted Answer

A)  0.142 
B)  0.145 
C)  0.148 
D)  0.151

Question 6

Consider a study in which two sets of 20 mice were given different amounts of caffeine in their drinking water. Members of the control group got none and members of the experimental group received 0.01% caffeine in their water. The number of minutes each mouse spent running on the wheel in their cage was measured over a series of 14 nights.
Describe why the appropriate sampling unit is the mean number of minutes for each of the 40 mice rather than the number of minutes during each of the 280 nights.
What are the sample sizes you would use when comparing this running data in the two groups?

Accepted Answer

The answer of Consider a study in which two sets...

Question 7

If the means of two populations are both significantly different from the same value, then they are significantly different from one another.

Accepted Answer

A) True 
 B)False

Question 8

Imagine a series of turbidity (cloudiness) measurements in the water from two different lakes. The measurements were taken over many different days (30 samples for each lake) and the figure shows the mean turbidity of those measurements along with bars representing 95% confidence intervals. What can we conclude about the appropriate null hypothesis and mean turbidity of the two lakes?
​
 ​

Accepted Answer

A)  Fail to reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. 
B)  Reject the null hypothesis, we have evidence that the turbidity differs between the lakes. 
C)  Reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. 
D)  We can't really tell from this figure whether the null hypothesis will be rejected or not.

Question 9

Consider urban ecologists who are interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. They plan to conduct a two-sample t-test and will assume that the population variances are equal. Their data are as follows:
Near (group 1): mean = 6.1, SD = 0.35, n = 9
Far (group 2): mean = 5.8, SD = 0.30, n = 12
What is the conclusion of the t-test?

Accepted Answer

A)  Fail to reject the null hypothesis, the mean number of eggs do not seem to differ in the two types of locations. 
B)  Fail to reject the null hypothesis, the mean number of eggs seem to differ in the two types of locations. 
C)  Reject the null hypothesis, the mean number of eggs do not seem to differ in the two types of locations. 
D)  Reject the null hypothesis, the mean number of eggs seem to differ in the two types of locations.

Question 10

Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows:
Near (group 1): mean = 6.1, SD = 0.35, n = 12
Far (group 2): mean = 5.8, SD = 0.30, n = 9
Based on the t-test statistic, and using your table of critical t-values, which of the following P-value ranges matches the one for the t-value?

Accepted Answer

A)  0.05 < p 
B)  0.02 < p < 0.05 
C)  0.01 < p < 0.02 
D)  p < 0.01

Question 11

Welch's t-test may only be used when the population variances are equal.

Accepted Answer

A) True 
 B)False

Question 12

Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. Based on the t-test statistic, which of the following best described the results of Chris's paired t-test?
?
Number of fish caught in six seines before and after drainage connection.

$\begin{array}{lll}
\underline {\text {Vial  } }&\underline {\text { Before } }&\underline {\text {  After } }\
1 & 24 & 20 \
2 & 35 & 31 \
3 & 64 & 59 \
4 & 51 & 52 \
5 & 25 & 28 \
6 & 48 & 39
\end{array}$ ?

Accepted Answer

A)  Fail to reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. 
B)  Fail to reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes. 
C)  Reject the null hypothesis, the storm did not seem to change the number of fish in the lakes. 
D)  Reject the null hypothesis, the storm seemed to reduce the number of fish in the lakes.

Question 13

Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the 95% confidence interval for the difference in the values?
?
Number of fish caught in six seines before and after drainage connection.

$\begin{array}{lll}
\underline {\text {Vial  } }&\underline {\text { Before } }&\underline {\text {  After } }\
1 & 24 & 20 \
2 & 35 & 31 \
3 & 64 & 59 \
4 & 51 & 52 \
5 & 25 & 22 \
6 & 48 & 39
\end{array}$

Accepted Answer

A)  -8.9 < ? < 0.9 
B)  -7.9 < ? < -0.1 
C)  -7.4 < ? < -0.6 
D)  -5.9 < ? < -2.1

Question 14

The paired t-test is essentially the same as a one-sample t-test of the set of differences with a hypothesized mean of zero for the differences.

Accepted Answer

A) True 
 B)False

Question 15

If we collect blood pressure values for a set of patients before talking with a psychiatrist and then blood pressure values from a second set of individuals after talking with a psychiatrist, what type of test is most appropriate?

Accepted Answer

A)  Paired test 
B)  Separation test 
C)  Temporal test 
D)  Two-sample test

Question 16

The F-test for comparing variances has a stringent assumption that is often not met in data sets we are analyzing. What is it?

Accepted Answer

A)  The data distributions must have equal means. 
B)  The data distributions must have equal variances. 
C)  The data must be binomially distributed. 
D)  The data must be normally distributed.

Question 17

Consider an urban ecologist who is interested in whether the presence of high-voltage power lines influences the number of eggs laid by birds nearby. She plans to conduct a two-sample t-test and will assume that the population variances are equal. Her data are as follows:
Near (group 1): mean = 6.1, SD = 0.35, n = 12
Far (group 2): mean = 5.8, SD = 0.30, n = 9
What is the pooled sample variance?

Accepted Answer

A)  0.099 
B)  0.104 
C)  0.109 
D)  0.114

Question 18

Which of the following is not an advantage of Levene's test versus the F-test as a test of population variances?

Accepted Answer

A)  It can compare more than two groups. 
B)  It is more robust to deviations from normality in the data distributions. 
C)  It is more robust to deviations from symmetry in the data distributions. 
D)  It uses the normal distribution instead of the F distribution.

Question 19

Consider a situation in which Chris predicts that an impending drainage connection will alter the number of fish in a set of six small lakes. She uses a large net (a seine) and counts the number of fish and obtains the values shown. What is the 95% confidence interval for the difference in the values?
?
Number of fish caught in six seines before and after drainage connection.

$\begin{array}{lll}
\underline {\text {Vial  } }&\underline {\text { Before } }&\underline {\text {  After } }\
1 & 24 & 20 \
2 & 35 & 31 \
3 & 64 & 59 \
4 & 51 & 52 \
5 & 25 & 28 \
6 & 48 & 39
\end{array}$

Accepted Answer

A)  -7.6 < ? < 1.55 
B)  -6.4 < ? < 1.36 
C)  -5.9 < ? < -1.26 
D)  -5.4 < ? < -1.76

Question 20

Imagine a series of turbidity (cloudiness) measurements in the water from two different lakes. The measurements were taken over many different days (30 samples for each lake) and the figure shows the mean turbidity of those measurements along with bars representing 95% confidence intervals. What can we conclude about the appropriate null hypothesis and mean turbidity of the two lakes?
​
 ​

Accepted Answer

A)  Fail to reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. 
B)  Reject the null hypothesis, we have evidence that the turbidity differs between the lakes. 
C)  Reject the null hypothesis, we lack evidence that the turbidity differs between the lakes. 
D)  We can't really tell from this figure whether the null hypothesis will be rejected or not.

Exam 12: Comparing Two Means

When we have two data sets that reveal 95% confidence intervals that differ from a hypothesized value and don't overlap, what conclusion can we make?

If the mean of population A is significantly different from 20, but the mean of group B is not significantly different from 20, then the mean of the two population are different from one another.

Draw a flowchart to describe the steps you would take when presented with data from two different groups, and the goal is to identify if the means of the groups differ. You may assume the data values are normally distributed. Include each possible statistical test.

If the means of two populations are both significantly different from the same value, then they are significantly different from one another.

Welch's t-test may only be used when the population variances are equal.

The paired t-test is essentially the same as a one-sample t-test of the set of differences with a hypothesized mean of zero for the differences.

If we collect blood pressure values for a set of patients before talking with a psychiatrist and then blood pressure values from a second set of individuals after talking with a psychiatrist, what type of test is most appropriate?

The F-test for comparing variances has a stringent assumption that is often not met in data sets we are analyzing. What is it?

Which of the following is not an advantage of Levene's test versus the F-test as a test of population variances?