Deck 10: Comparing Two Means

Question 1

A researcher was interested in stress levels of lecturers during lecturers. She took the same group of 8 lecturers and measured their anxiety (out of 15) during a normal lecture and again in a lecture in which she had paid students to be disruptive and misbehave. Based on the SPSS output, how would you interpret these results?

A)There were no significant differences between anxiety levels in normal lectures and in those in which students misbehaved.
B)We can't tell any of the above from the output given.
C)Anxiety levels were significantly higher in lectures in which students misbehaved.
D)Anxiety levels were significantly lower in lectures in which students misbehaved.

Answer 1

C

Question 2

An paired-samples t-test is used to test for:

A)Differences between means of groups containing different entities when the sampling distribution is normally distributed, and the data have equal variances and are at least interval.
B)Differences between means of groups containing the same entities when the sampling distribution is normally distributed, and the data have equal variances and are at least interval.
C)Differences between means of groups containing different entities when the sampling distribution is not normally distributed.
D)Differences between means of groups containing the same entities when the sampling distribution is not normally distributed and the data do not have unequal variances.

Answer 2

B

Question 3

The t-statistic:

A)When significant, indicates an important finding.
B)Is accurate only when using large samples.
C)Is the standard deviation of the sampling distribution of a statistic.
D)Is the ratio of the systematic variation to the unsystematic variation.

Answer 3

D

Question 4

What does the independent t-test test assume?

A)There are no differences between the mean scores.
B)The data are normally distributed
C)The sampling distribution is normally distributed.
D)The means of two sets of scores are correlated.

Question 5

A recent study investigated whether vodka is less likely to give you a hangover than wine. Twenty participants on a night out were asked to drink only vodka for the whole evening then rate how they felt the next day out of 10 (0 = I feel fantastic, 10 = I can't move my head in case it explodes). The following month, they were asked to do the same again, only this time they were asked to drink only white wine. The t-score was 2.56. Which of the sentences below is correct?

A)It is significant at the 1% level with a two-tailed test.
B)It is not significant with a two-tailed test.
C)It is significant at the 5% level but not the 1% level with a two-tailed test.
D)It is not significant with a one-tailed test.

Question 6

A small standard error of differences tells us:

A)That the differences between scores are not normally distributed.
B)That the differences between scores are normally distributed.
C)That most pairs of samples from a population will have very similar means.
D)That sample means can deviate quite a lot from the population mean and so differences between pairs of samples can be quite large by chance alone.

Question 7

Participants rated their mood score out of 20 before and after listening to Reign in Blood by the thrash metal band Slayer. $\begin{array} { | c | c | } \hline \text { Before Listening to Slayer } & \text { After Listening to } \mathbf { S l a y e r } \\\hline 5 & 14 \\\hline \mathbf { 8 } & \mathbf { 5 } \\\hline \mathbf { 9 } & 17 \\\hline 4 & 18 \\\hline \mathbf { 3 } & \mathbf { 8 } \\\hline 15 & 19 \\\hline 12 & 14 \\\hline \mathbf { 6 } & 16 \\\hline\end{array}$

- What is the null hypothesis of this study?

A)Listening to Slayer is no better than listening to no music at improving mood score.
B)Listening to Slayer does not affect mood.
C)Listening to Slayer increases mood score.
D)Listening to Slayer decreases mood score.

Question 8

The degrees of freedom for the paired samples t-test are:

A)N - 2
B) $\surd$ N - 1
C)N - 1
D)N

Question 9

A researcher measured a group of people's physiological reactions while watching horror films and compared them to when watching comedy films. The resulting data were normally distributed. What test should be used to analyse the data?

A)Independent t-test.
B)Mann-Whitney test.
C)Wilcoxon signed-rank test.
D)Paired-samples (dependent or related) t-test.

Question 10

Which of the following statements about the t distribution is correct?

A)It is skewed.
B)In small samples it is narrower than the normal distribution
C)It follows an exponential curve.
D)As the degrees of freedom increase, the distribution becomes closer to normal

Question 11

A researcher was interested in the effects of emotion-evoking music on exam performance. Before their SPSS exam, a lecturer took one group of students to a room in which calming music was being played. A different group of students were taken to another room in which the 'death march' was being played. The students then did the exam and their marks were noted. The SPSS output is below. The experimenter made no predictions about which form of support would produce the best exam performance. What should he report? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Statistics }$
$\begin{array}{l}\begin{array} { | l l | r | r | r | r | } \hline & \text { Emotional Support } & { \mathrm { N } } &{ \text { Mean } } & { \begin{array} { c } \text { Std. } \\\text { Deviation }\end{array} } & { \begin{array} { c } \text { Std. Error } \\\text { Mean }\end{array} } \\\hline \text { SPSS Exam Mark } & \text { Positive Support } & 20 & 65.1500 & 5.0396 & 1.1269 \\& \text { Negative Support } & 20 & 57.8000 & 15.2129 & 3.4017 \\\hline\end{array}\end{array}$

A)Marks for students receiving positive music before the exam did not significantly differ from students receiving negative music, t(23.12) = 2.05, p = .052.
B)Students receiving positive music before the exam did significantly better than those receiving negative music, t(38) = 2.05, p = .047.
C)Marks for students receiving positive music before the exam did not significantly differ from students receiving negative music, t(38) = 2.05, p = .047.
D)Students receiving positive music before the exam did significantly better than those receiving negative music, t(23.12) = 2.05, p < .05, one-tailed.

Question 12

Which of the following sentences is an accurate description of the standard error?

A)It is the standard deviation of the sampling distribution of a statistic.
B)It is the same as the standard deviation.
C)It is the observed difference between sample means minus the expected difference between population means (if the null hypothesis is true).
D)The standard deviation squared.

Question 13

An independent t-test is used to test for:

A)Differences between means of groups containing different entities when the data are not normally distributed or have unequal variances.
B)Differences between means of groups containing different entities when the sampling distribution is normal, the groups have equal variances and data are at least interval.
C)Differences between means of groups containing the same entities when the data are normally distributed, have equal variances and data are at least interval.
D)Differences between means of groups containing the same entities when the sampling distribution is not normally distributed and the data do not have unequal variances.

Question 14

When conducting an independent t-test, what is the dependent variable?

A)The term 'dependent variable' does not apply to the t-test.
B)One of the independent variables becomes the dependent variable in the analysis.
C)The experimental conditions
D)The scores

Question 15

Participants rated their mood score out of 20 before and after listening to Reign in Blood by the thrash metal band Slayer. $\begin{array} { | c | c | } \hline \text { Before Listening to Slayer } & \text { After Listening to } \mathbf { S l a y e r } \\\hline 5 & 14 \\\hline \mathbf { 8 } & \mathbf { 5 } \\\hline \mathbf { 9 } & 17 \\\hline 4 & 18 \\\hline \mathbf { 3 } & \mathbf { 8 } \\\hline 15 & 19 \\\hline 12 & 14 \\\hline \mathbf { 6 } & 16 \\\hline\end{array}$

-What are the degrees of freedom for this study?

A)7
B)8
C)16
D)15

Question 16

Two samples of data are collected and the sample means calculated. If the samples come from the same population, then:

A)Their means should be roughly equal.
B)Their means should differ significantly.
C)The experiment is unreliable.
D)The difference between the samples we have collected is likely to be larger than we would expect based on the standard error.

Question 17

Other things being equal, compared to the paired-samples (or dependent) t-test, the independent t-test:

A)Is less robust.
B)Has less power to find an effect.
C)Has more power to find an effect.
D)Has the same amount of power, the data are just collected differently.

Question 18

If you use a paired samples t-test:

A)The same participants take part in both experimental conditions.
B)Other things being equal, you do not need as many participants as you would for an independent samples design.
C)All of these are correct.
D)There ought to be less unsystematic variance compared to the independent t-test.

Question 19

A psychologist was interested in whether there was a gender difference in the use of email. She hypothesized that because women are generally better communicators than men, they would spend longer using email than their male counterparts. To test this hypothesis, the researcher sat by the email computers in her research methods laboratory and when someone started using email, she noted whether they were male or female and then timed how long they spent using email (in minutes). What should she report? $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Group Statistics }$
$\begin{array}{|ll|r|r|r|r|} \hline & \text { Gender } & \mathrm{N} & \text { Mean } & \text { Std. Deviation } & {\begin{array}{c}\text { Std. Error } \\\text { Mean }\end{array}} \\\hline \text { Time Using Email (Day 2) } & \text { Male } & 8 & 5.0000 & 4.50397 & 1.59239 \\& \text { Female } & 8 & 32.0000 & 40.04640 & 14.15854\\\hline \end{array}$

A)Females and males did not significantly differ in the time spent using email, t(14) = -1.90, p = .10.
B)Females and males did not significantly differ in the time spent using email, t(7.18) = -1.90, p = .10.
C)Females spent significantly longer using email than males, t(14) = -1.90, p < .05.
D)Females and males did not significantly differ in the time spent using email, t(7.18) = -1.90, p < .05, one-tailed.

Question 20

What does the variance sum law state?

A)That the variance of a difference between two independent variables is equal to the sum of their variances.
B)That the sum of the variances of two independent variables is larger than the sum of their individual variances.
C)That the variance of a difference between two independent variables is larger than the sum of their variances.
D)That the variance of a difference between two independent variables is smaller than the sum of their variances.