Deck 7: The T Test for Independent Groups

Question 1

A business statistician wishes to determine whether current unemployment rates differ between former communist countries and European/Asian nations that have not been under communist control. A sample of 10 countries each was randomly chosen from all eligible countries. The data are as follows: $\begin{array} { c c } \hline \text { Former Communist } & \text { Not Former Communist } \\\text { (\%) } & \text { (\%) } \\\hline 23 & 12 \\13 & 8 \\33 & 9 \\21 & 14 \\17 & 7 \\24 & 8 \\12 & 10 \\18 & 11 \\27 & 12 \\16 & 7 \\\hline\end{array}$

-Are the mean percentages significantly different?

A)yes, at p < .05
B)yes, at p < .01
C)yes, at p < .001
D)no, at p > .05

Answer 1

yes, at p < .001

Question 2

A business statistician wishes to determine whether current unemployment rates differ between former communist countries and European/Asian nations that have not been under communist control. A sample of 10 countries each was randomly chosen from all eligible countries. The data are as follows: $\begin{array} { c c } \hline \text { Former Communist } & \text { Not Former Communist } \\\text { (\%) } & \text { (\%) } \\\hline 23 & 12 \\13 & 8 \\33 & 9 \\21 & 14 \\17 & 7 \\24 & 8 \\12 & 10 \\18 & 11 \\27 & 12 \\16 & 7 \\\hline\end{array}$

-The degrees of freedom for this problem are

A)20
B)18
C)10
D)9

Answer 2

18

Question 3

The Food and Drug Administration wishes to determine whether the claim that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self-reported colds is recorded after 3 years. $\begin{array}{cc}\text { Vitamin C } & \text { Placebo } \\\hline 3 & 8 \\8 & 8 \\6 & 7 \\7 & 10 \\4 & 11 \\9 & 4\\2 & 3 \\5 & 7 \\7 & 6 \\11 & 8 \\10 & 4 \\8 & 10 \\7 & 6 \\6 & 8 \\7 & 5\\\hline\end{array}$

-What significance level should be reported?

A)p < .05
B)p < .01
C)p < .001
D)p > .05

Answer 3

p > .05

Question 4

The Food and Drug Administration wishes to determine whether the claim that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self-reported colds is recorded after 3 years. $\begin{array}{cc}\text { Vitamin C } & \text { Placebo } \\\hline 3 & 8 \\8 & 8 \\6 & 7 \\7 & 10 \\4 & 11 \\9 & 4\\2 & 3 \\5 & 7 \\7 & 6 \\11 & 8 \\10 & 4 \\8 & 10 \\7 & 6 \\6 & 8 \\7 & 5\\\hline\end{array}$

-The value of the numerator (either or -) in the t test formula for this problem is

A)0.378
B)6.67
C)7.00
D).051

Question 5

A business statistician wishes to determine whether current unemployment rates differ between former communist countries and European/Asian nations that have not been under communist control. A sample of 10 countries each was randomly chosen from all eligible countries. The data are as follows: $\begin{array} { c c } \hline \text { Former Communist } & \text { Not Former Communist } \\\text { (\%) } & \text { (\%) } \\\hline 23 & 12 \\13 & 8 \\33 & 9 \\21 & 14 \\17 & 7 \\24 & 8 \\12 & 10 \\18 & 11 \\27 & 12 \\16 & 7 \\\hline\end{array}$

-The correct statistical decision would be

A)retain the null hypothesis
B)reject the null hypothesis
C)retain the alternative hypothesis
D)reject the directional null hypothesis

Question 6

The Food and Drug Administration wishes to determine whether the claim that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self-reported colds is recorded after 3 years. $\begin{array}{cc}\text { Vitamin C } & \text { Placebo } \\\hline 3 & 8 \\8 & 8 \\6 & 7 \\7 & 10 \\4 & 11 \\9 & 4\\2 & 3 \\5 & 7 \\7 & 6 \\11 & 8 \\10 & 4 \\8 & 10 \\7 & 6 \\6 & 8 \\7 & 5\\\hline\end{array}$

-The degrees of freedom for this problem are

A)30
B)28
C)15
D)14

Question 7

The Food and Drug Administration wishes to determine whether the claim that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self-reported colds is recorded after 3 years. $\begin{array}{cc}\text { Vitamin C } & \text { Placebo } \\\hline 3 & 8 \\8 & 8 \\6 & 7 \\7 & 10 \\4 & 11 \\9 & 4\\2 & 3 \\5 & 7 \\7 & 6 \\11 & 8 \\10 & 4 \\8 & 10 \\7 & 6 \\6 & 8 \\7 & 5\\\hline\end{array}$

-The derived t value (either + or -) for this problem is

A)0.708
B)0.378
C)0.333
D)0.05

Question 8

A business statistician wishes to determine whether current unemployment rates differ between former communist countries and European/Asian nations that have not been under communist control. A sample of 10 countries each was randomly chosen from all eligible countries. The data are as follows: $\begin{array} { c c } \hline \text { Former Communist } & \text { Not Former Communist } \\\text { (\%) } & \text { (\%) } \\\hline 23 & 12 \\13 & 8 \\33 & 9 \\21 & 14 \\17 & 7 \\24 & 8 \\12 & 10 \\18 & 11 \\27 & 12 \\16 & 7 \\\hline\end{array}$

-The appropriate conclusion of this statistical analysis would be

A)The mean unemployment rate (20.4%) in former communist countries is significantly greater (p < .001) than the mean unemployment rate (9.8%) in countries not formerly under communist control.
B)The mean unemployment rate (9.8%) in former communist countries is significantly greater (p < .001) than the mean unemployment rate (20.4%) in countries not formerly under communist control.
C)The mean unemployment rate (20.4%) in former communist countries is significantly greater (p < .05) than the mean unemployment rate (9.8%) in countries not formerly under communist control.
D)The mean unemployment rate (20.4%) in former communist countries is not significantly greater (p > .05) than the mean unemployment rate (9.8%) in countries not formerly under communist control.

Question 9

A business statistician wishes to determine whether current unemployment rates differ between former communist countries and European/Asian nations that have not been under communist control. A sample of 10 countries each was randomly chosen from all eligible countries. The data are as follows: $\begin{array} { c c } \hline \text { Former Communist } & \text { Not Former Communist } \\\text { (\%) } & \text { (\%) } \\\hline 23 & 12 \\13 & 8 \\33 & 9 \\21 & 14 \\17 & 7 \\24 & 8 \\12 & 10 \\18 & 11 \\27 & 12 \\16 & 7 \\\hline\end{array}$

-The derived t value for this problem is

A)7.338
B)4.816
C)11.373
D)12.000

Question 10

A psychiatrist is interested in the effects of a new drug for the control of depression. In a clinical trial, 18 depressed patients were randomly assigned to one of two groups, either the drug group or the placebo group. One half hour after the administration of the drug or placebo, their depression was measured by the Coolidge Axis II Inventory's Depression scale and reported as T scores (M = 50, SD = 10). $\begin{array} { c c } \hline \text { Drug } & \text { Placebo } \\\hline 52 & 65 \\53 & 59 \\58 & 68 \\50 & 53 \\53 & 59 \\58 & 67 \\55 & 61 \\66 & 70 \\53 & 62 \\\hline\end{array}$

-The degrees of freedom for this problem are

A)18
B)16
C)8
D)20

Question 11

A psychiatrist is interested in the effects of a new drug for the control of depression. In a clinical trial, 18 depressed patients were randomly assigned to one of two groups, either the drug group or the placebo group. One half hour after the administration of the drug or placebo, their depression was measured by the Coolidge Axis II Inventory's Depression scale and reported as T scores (M = 50, SD = 10). $\begin{array} { c c } \hline \text { Drug } & \text { Placebo } \\\hline 52 & 65 \\53 & 59 \\58 & 68 \\50 & 53 \\53 & 59 \\58 & 67 \\55 & 61 \\66 & 70 \\53 & 62 \\\hline\end{array}$

-The value of the numerator in the t formula for this problem (either or -) is

A)3.058
B)55.33
C)62.67
D)7.33

Question 12

A psychiatrist is interested in the effects of a new drug for the control of depression. In a clinical trial, 18 depressed patients were randomly assigned to one of two groups, either the drug group or the placebo group. One half hour after the administration of the drug or placebo, their depression was measured by the Coolidge Axis II Inventory's Depression scale and reported as T scores (M = 50, SD = 10). $\begin{array} { c c } \hline \text { Drug } & \text { Placebo } \\\hline 52 & 65 \\53 & 59 \\58 & 68 \\50 & 53 \\53 & 59 \\58 & 67 \\55 & 61 \\66 & 70 \\53 & 62 \\\hline\end{array}$

-The overall results would mean that

A)the new drug significantly lowers anxiety levels compared to a placebo
B)the new drug lowers anxiety levels by a factor of .01
C)the new drug is significant
D)the new drug lowers anxiety levels compared to a placebo but not significantly

Question 13

A psychiatrist is interested in the effects of a new drug for the control of depression. In a clinical trial, 18 depressed patients were randomly assigned to one of two groups, either the drug group or the placebo group. One half hour after the administration of the drug or placebo, their depression was measured by the Coolidge Axis II Inventory's Depression scale and reported as T scores (M = 50, SD = 10). $\begin{array} { c c } \hline \text { Drug } & \text { Placebo } \\\hline 52 & 65 \\53 & 59 \\58 & 68 \\50 & 53 \\53 & 59 \\58 & 67 \\55 & 61 \\66 & 70 \\53 & 62 \\\hline\end{array}$

-The derived t value for this problem (either or ) is

A)3.058
B)7.33
C).008
D)2.120

Question 14

A psychiatrist is interested in the effects of a new drug for the control of depression. In a clinical trial, 18 depressed patients were randomly assigned to one of two groups, either the drug group or the placebo group. One half hour after the administration of the drug or placebo, their depression was measured by the Coolidge Axis II Inventory's Depression scale and reported as T scores (M = 50, SD = 10). $\begin{array} { c c } \hline \text { Drug } & \text { Placebo } \\\hline 52 & 65 \\53 & 59 \\58 & 68 \\50 & 53 \\53 & 59 \\58 & 67 \\55 & 61 \\66 & 70 \\53 & 62 \\\hline\end{array}$

-The correct statistical decision would be to

A)reject the null hypothesis at p < .05 (although it would be reported significant at p < .01)
B)retain the null hypothesis (p > .05)
C)reject the null hypothesis at p < .05 (although it would be reported significant at p < .001)

Question 15

The Food and Drug Administration wishes to determine whether the claim that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self-reported colds is recorded after 3 years. $\begin{array}{cc}\text { Vitamin C } & \text { Placebo } \\\hline 3 & 8 \\8 & 8 \\6 & 7 \\7 & 10 \\4 & 11 \\9 & 4\\2 & 3 \\5 & 7 \\7 & 6 \\11 & 8 \\10 & 4 \\8 & 10 \\7 & 6 \\6 & 8 \\7 & 5\\\hline\end{array}$

-What can be concluded from the statistical analysis of this problem?

A)the null hypothesis cannot be rejected
B)Vitamin C doesn't seem to prevent colds any better than a placebo
C)the mean number of colds is not significantly different between the two groups
D)all of the above are true