Part A: Review of Chapters 1-10 (10 @ 2 = 20 points)
For each of the 10 statements below, indicate whether the statement is true or false.
Explain your decision about the truth of the statement with reference to the bolded terms.
A1: An operational definition of a dependent variable is also known as a confounding
False. An operational definition refers to the procedures for measuring or manipulating a variable.
A dependent variable is an outcome measure related to or caused by an independent variable. A
confounding variable is a variable that systematically covaries with an independent variable so
that it is not possible to know whether the confounding variable or the independent variable leads
to changes in the dependent variable. Therefore, the statement is false because a confounding
variable is not a dependent variable.
A2. Sometimes a positively skewed distribution is the result of a floor effect.
True. A positively skewed distribution has a tail to the right side of the distribution representing
the high scores. A floor effect results when there is a limit on the low scores in the distribution so
that there is no tail of extreme scores on the left side of the distribution. Thus, there is an
asymmetry (skew) in the distribution of scores with a tail on the right but not on the left.
A3. A time series plot of a nonlinear relation is often shown as a Pareto chart.
False. A time series plot graphs a scale variable on the y-axis as a function of a unit of time on the
x-axis. A nonlinear relation is one in which the function relating the y-axis scores to the x-axis
time units does not consistently increase or decrease per unit of time. A Pareto chart is a bar
graph with a nominal variable on the x-axis that is ordered such that the y-values decrease from
highest to lowest across the levels of the nominal variable. Therefore, the statement is false
because the x-axis scale of time in a time series plot is not nominal.
A4. The standard deviation is equal to the square root of variance and is a measure of the
typical amount a score deviates from the mean.
True. The variance is obtained by squaring deviations from the mean. The standard deviation
“unsquares” the squared deviations from the mean to yield the typical amount that a score
deviates from the mean.
A5. A researcher who reports a statistically significant result that cannot be replicated has likely
made a Type 1 error.
True. A researcher who reports a statistically significant result has rejected the null hypothesis.
A Type 1 error occurs when the null hypothesis is rejected despite the null hypothesis being true.
If other researchers cannot find evidence to reject the null hypothesis when repeating the original
study, then the original report of a statistically significant result is likely a Type 1 error.
A6. According to the central limit theorem, a distribution of sample means has larger
variance than does a distribution of scores in a population.
False. The central limit theorem states that a distribution of sample means approaches a normal
curve as sample size increases. This is true whether or not the original population of scores is
normally distributed. A distribution of sample means is less variable than a distribution of
individual scores because the sample scores will reduce the impact of extreme individual scores.
A7. If the percentage of scores falling between the mean and a z score of 0.50 is 19.15, then the
percentage of scores falling below a z score of 0.50 is 19.15. False. There are 50% of scores below the mean (z = 0) so the total percentage of scores below a z
score of .50 is 50 + 19.15 = 69.15.
A8. A confidence interval is centred around a population mean so that the width of the interval
is equal for a 99% confidence interval and a 95% confidence interval.
False. A confidence interval is an interval estimate that is based on a sample mean. The interval
includes the population mean a percentage of time where a given sample size is repeatedly drawn
from the population. The margin of error will be larger for a 99% confidence interval than for a
95% because the critical statistic value that is used in computing the upper and lower limits is
larger for the 99% confidence interval than for the 95% confidence interval.
A9. A single-sample t test on the scores of 10 participants will have the same number of
degrees of freedom as a paired-samples t test on the scores of 10 participants.
True. Both the single-sample t test and the paired-samples t test have N-1 degrees of freedom.
The paired-samples t test requires first calculating the difference scores for each individual, and
once that step has been completed, the two tests are identical.
A10. When calculating the pooled variance for an independent-samples t-test, more weight is
given to the larger sample.
True. When calculating the pooled variance, the variance of each sample is multiplied by the df
for that sample divided by the total df. If the samples differ in the number of scores, then the df
for the larger sample will be larger than for the smaller sample. Thus, the ratio of the sample df
to the total df will be larger for the larger sample.
B. Questions based on chapters 13, 14, and 15. (20 points)
Clearly indicate all the steps used in your computations.
Use alpha = .05 for a two-tailed test in all statistical decisions.
Do NOT use ‘yes’ or ‘no’ as an answer—always explain your answers.
B1. A social psychologist studied the relationship between a mother’s happiness and the number
of children she has.The results for 5 mothers a