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

PSY 201 1
Introduction to Statistics in Psychology: PSY 201
Greg Francis, PhD
Department of Psychological Sciences
Psychological Sciences Building, Room 3174
(765) 494-6934
email: gfrancis@purdue.edu
http://www1.psych.purdue.edu/∼gfrancis/Classes/PSY201/
Homework 8
Due: 18 October 2009
Hand in your answers on a separate sheet of paper.
(1) A researcher develops a new theory that predicts that vegetarians will have more of a particular
vitamin in their blood than non-vegetarians. An experiment is conducted and vegetarians do have
more of the vitamin, but the difference is not significant. The probability value is 0.13. Should the
experimenter’s confidence in the theory increase, decrease, or stay the same Explain your choice.
(2) A significance test is performed and p = .20. Why can’t the experimenter claim that the
probability that the null hypothesis is true is .20
(3) You choose an alpha level of .01 and then analyze your data.
a) What is the probability that you will make a Type I error given that the null hypothesis is
true
b) What is the probability that you will make a Type I error given that the null hypothesis is
false
(4) Although there is a popular belief that herbal remedies such as Ginkgo biloba and Ginseng
may improve learning and memory in healthy adults, these effects are usually not supported by
well-controlled research (Peresson et al., 2004). In a typical study, a researcher obtains a sample
of n = 36 participants and has each person take the herbal supplements every day for 90 days. At
the end of the 90 days, each person takes a standardized memory test. For the general population,
scores from the test are normally distributed with a mean of µ = 80 and a standard deviation of
σ = 18. The sample of research participants had an average of X = 84.
a) In a sentence, state the null hypothesis being tested.
b) Using symbols, state the null hypothesis and the alternative hypothesis.
c) Conduct the hypothesis using a two-tailed test with α = 0.05.

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(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.

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(9) Montarello and Martins (2005) found that fifth-grade students completed more mathematics
problems correctly when simple problems were mixed in with their regular math assignments. To
further explore this phenomenon, suppose that a researcher selects a standardized mathematics
achievement test that produces a normal distribution of scores with a mean of µ = 100 and a
stanard deviation of σ = 18. The researcher modifies the test by inserting a set of very easy
problems among the standardized questions, and gives the modified test to a sample of n = 36
students. If the average test score for the sample is X = 104, is this result sufficient to conclude
that inserting the easy questions improves performance Use a one-tailed test with α = 0.01
(10) Compute the t values that form the boundaries of the critical region for a two-tailed test with
α = 0.05 for each of the following df values.
a) df = 8
b) df = 15
c) df = 24
(11) A sample is randomly selected from a population with a mean of µ = 50, and a treatment
is administered to the individuals in the sample. After treatment, the sample is found to have a
mean of X = 56 with a standard deviation of s = 8.
a) If there are n = 4 individuals in the sample, are the data sufficient to reject H 0 and conclude
that the treatment has a significant effect using a two-tailed test with α = 0.05
b) If there are n = 16 individuals in the sample, are the data sufficient to reject H 0 and conclude
that the treatment has a significant effect Again, assume a two-tailed test with α = 0.05.
(12) Last fall, a sample of n = 36 freshmen was selected to participate in a new 4-hour training
program designed to improve study skills. To evaluate the effectiveness of the new program, the
sample was compared with the rest of the freshman class. All freshmen must take the same English
Language Skills course, and the mean score on the final exam for the entire freshman class of
µ = 75. The students in the new program had a mean score of X = 79.4 with a standard deviation
of s = 18.
a) On the basis of this data, can the college conclude that the students in the new program
performed significantly better than the rest of the freshman class Use a one-tailed test with
α = 0.05.
b) On the basis of this data, can the college conclude that the students in the new program are
significantly different from the rest of the freshman class Use a two-tailed test with α = 0.05.
(13) The librarian at the local elementary school claims that, on average, the books in the library
are more than 20 years old. To test this claim, a student takes a sample of n = 30 books and
records the publication date for each. The sample produces an average age of X = 23.8 years with
a variance of s 2 = 67.5. Use this sample to conduct a one-tailed test with α = 0.01 to determine
whether the average age of the library books is significantly greater than 20 years.

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(14) Numerous studies have shown that IQ scores have been increasing, generation by generation,
for years (Flynn, 1984, 1999). The increase is called the Flynn Effect, and the data indicate that the
increase appears to be about 7 points per decade. To demonstrate this phenomenon, a researcher
obtains an IQ test that was written in 1980. At the time the test was prepared, it was standardized
to produce a population mean of µ = 100. The researcher administers the test to a random sample
of n = 16 of today’s high school students and obtains a sample mean IQ of X = 121 with s = 6.32.
Is this result sufficient to conclude that today’s sample scored significantly higher than would be
expected from a population with µ = 100 Use a one-tailed test with α = 0.01.