Introduction to Statistics in Psychology: PSY 201 - Department of ...

PSY 201 2
(5) A researcher is testing the effectiveness of a new drug that is intended to improve learning and
memory performance. A sample of n = 16 rats is obtained, and the rats are administered the drug
and then tested on a standardized learning task. For the general population of rats (with no drugs)
the average score on the standardized task is µ = 50 with a standard deviation of σ = 10. The
distribution of test scores is normal.
a) If the drug has a 4-point effect and produces a mean score of X = 54 for the sample, is this
sufficient to conclude that there is a significant effect using a two-tailed test with α = 0.05
b) If there is a 6-point effect with a mean score of X = 56, is this sufficient to conclude that
there is a significant effect using a two-tailed test with α = 0.05
(6) State College is evaluating a new English composition course for freshmen. A random sample
of n = 25 freshmen is obtained and the students are placed in the course during their first semester.
One year later, a writing sample is obtained for each student and the writing samples are graded
using a standardized evaluation technique. The average score for the sample if X = 76. For the
general population of college students, writing score form a normal distribution with a mean of
µ = 70.
a) If the writing scores for the population have a standard deviation of σ = 20, does the sample
provide enough evidence to conclude that the new composition course has a significant effect
Assume a two-tailed test with α = 0.05.
b) If the population standard deviation is σ = 10, is the sample sufficient to demonstrate a
significant effect Again, assume a two-tailed test with α = 0.05.
c) Briefly explain why you reached different conclusions for part (a) and part (b).
(7) A psychologist is investigating the hypothesis that children who grow up as the only child in the
household develop different personality characteristics than those who grow up in larger families. A
sample of n = 30 only children is obtained and each child is given a standardized personality test.
For the general population, scores on the test from a normal distribution with a mean of µ = 50
and a standard deviation of σ = 15. If the mean for the mean for the sample is X = 58, can the
researcher conclude that there is a significant difference in personality between only children and
the rest of the population Use a two-tailed test with α = 0.05.
(8) A researcher is testing the hypothesis that consuming a sports drink during exercise will improve
endurance. A sample of n = 50 male college students is obtained and each student is given a series
of three endurance tasks and asked to consume 4 ounces of the drink during each break between
tasks. The overall endurance score for this sample is X = 53. For the general population, without
any sports drink, the scores for this task average µ = 50 with a standard deviation of σ = 12.
a) Can the researcher conclude that endurance scores with the sports drink are significantly
higher than scores without the drink Use a one-tailed test with α = 0.05.
b) Can the researcher conclude that endurance scores with the sports drink are significantly
higher than scores without the drink Use a two-tailed test with α = 0.05.
c) You should find that the two tests lead to different conclusions. Explain why.