STATISTICS FOR THE BEHAVIORAL
SCIENCES EXAM 3 QUESTION BANK 2026
RESEARCH ANALYSIS MATERIAL
SOLUTIONS UPDATED A+
◉ Selecting an Alpha Level
Answer: The primary concern when selecting an alpha level is to
minimize the risk of a Type I error. Thus, alpha levels tend to be very
small probability values. By convention, the largest permissible
value is α = .05.
However, as the alpha level is lowered, the hypothesis test demands
more evidence from the research results.
◉ More about Hypothesis Tests
Answer: A result is said to be significant or statistically significant if
it is very unlikely to occur when the null hypothesis is true.
That is, the result is sufficient to reject the null hypothesis.
Thus, a treatment has a significant effect if the decision from the
hypothesis test is to reject H0.
◉ Factors That Influence a Hypothesis Test
,Answer: The final decision in a hypothesis test is determined by the
value obtained for the z-score statistic. Two factors help determine
whether the z-score will be large enough to reject H0.
In a hypothesis test, higher variability can reduce the chances of
finding a significant treatment effect.
Increasing the number of scores in the sample produces a smaller
standard error and a larger value for the z-score.
◉ Assumptions for Hypothesis Tests with z-Scores
Answer: It is assumed that the participants used in the study were
selected randomly.
The values in the sample must consist of independent observations.
Two events (or observations) are independent if the occurrence of
the first event has no effect on the probability of the second event.
The standard deviation for the unknown population (after
treatment) is assumed to be the same as it was for the population
before treatment.
To evaluate hypotheses with z-scores, we have used the unit normal
table to identify the critical region. This table can be used only if the
distribution of sample means is normal.
◉ Directional Tests
, Answer: In a directional hypothesis test, or a one-tailed test, the
statistical hypotheses (H0 and H1) specify either an increase or a
decrease in the population mean. That is, they make a statement
about the direction of the effect.
When a specific direction is expected for the treatment effect, it is
possible for the researcher to perform a directional test. The first
step (and the most critical step) is to state the statistical hypotheses.
The null hypothesis states that there is no treatment effect and that
the alternative hypothesis says that there is an effect. The two
hypotheses are mutually exclusive and cover all of the possibilities.
The critical region is defined by sample outcomes that are very
unlikely to occur if the null hypothesis is true (that is, if the
treatment has no effect). Because the critical region is contained in
one tail of the distribution, a directional test is commonly called a
one-tailed test. Also note that the proportion specified by the alpha
level is not divided between two tails, but rather is contained
entirely in one tail.
◉ Comparison of One-Tailed vs. Two-Tailed Tests
Answer: The major distinction between one-tailed and two-tailed
tests is in the criteria they use for rejecting H0.
A one-tailed test allows you to reject the null hypothesis when the
difference between the sample and the population is relatively small,
provided the difference is in the specified direction.
SCIENCES EXAM 3 QUESTION BANK 2026
RESEARCH ANALYSIS MATERIAL
SOLUTIONS UPDATED A+
◉ Selecting an Alpha Level
Answer: The primary concern when selecting an alpha level is to
minimize the risk of a Type I error. Thus, alpha levels tend to be very
small probability values. By convention, the largest permissible
value is α = .05.
However, as the alpha level is lowered, the hypothesis test demands
more evidence from the research results.
◉ More about Hypothesis Tests
Answer: A result is said to be significant or statistically significant if
it is very unlikely to occur when the null hypothesis is true.
That is, the result is sufficient to reject the null hypothesis.
Thus, a treatment has a significant effect if the decision from the
hypothesis test is to reject H0.
◉ Factors That Influence a Hypothesis Test
,Answer: The final decision in a hypothesis test is determined by the
value obtained for the z-score statistic. Two factors help determine
whether the z-score will be large enough to reject H0.
In a hypothesis test, higher variability can reduce the chances of
finding a significant treatment effect.
Increasing the number of scores in the sample produces a smaller
standard error and a larger value for the z-score.
◉ Assumptions for Hypothesis Tests with z-Scores
Answer: It is assumed that the participants used in the study were
selected randomly.
The values in the sample must consist of independent observations.
Two events (or observations) are independent if the occurrence of
the first event has no effect on the probability of the second event.
The standard deviation for the unknown population (after
treatment) is assumed to be the same as it was for the population
before treatment.
To evaluate hypotheses with z-scores, we have used the unit normal
table to identify the critical region. This table can be used only if the
distribution of sample means is normal.
◉ Directional Tests
, Answer: In a directional hypothesis test, or a one-tailed test, the
statistical hypotheses (H0 and H1) specify either an increase or a
decrease in the population mean. That is, they make a statement
about the direction of the effect.
When a specific direction is expected for the treatment effect, it is
possible for the researcher to perform a directional test. The first
step (and the most critical step) is to state the statistical hypotheses.
The null hypothesis states that there is no treatment effect and that
the alternative hypothesis says that there is an effect. The two
hypotheses are mutually exclusive and cover all of the possibilities.
The critical region is defined by sample outcomes that are very
unlikely to occur if the null hypothesis is true (that is, if the
treatment has no effect). Because the critical region is contained in
one tail of the distribution, a directional test is commonly called a
one-tailed test. Also note that the proportion specified by the alpha
level is not divided between two tails, but rather is contained
entirely in one tail.
◉ Comparison of One-Tailed vs. Two-Tailed Tests
Answer: The major distinction between one-tailed and two-tailed
tests is in the criteria they use for rejecting H0.
A one-tailed test allows you to reject the null hypothesis when the
difference between the sample and the population is relatively small,
provided the difference is in the specified direction.
