PSYC-FP4700 Assessment 3 Worksheet
Assessment 3 – Hypothesis, Effect Size, Power, and t
Tests
Complete the following problems within this Word document. Do not submit other files. Show
your work for problem sets that require calculations. Ensure that your answer to each problem is
clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Hypothesis, Effect Size, and Power
Problem Set 3.1: Sampling Distribution of the Mean Exercise
Criterion: Interpret population mean and variance.
Instructions: Read the information below and answer the questions.
Suppose a researcher wants to learn more about the mean attention span of individuals in some
hypothetical population. The researcher cites that the attention span (the time in minutes
attending to some task) in this population is normally distributed with the following
2
characteristics: 20 36 (μ σ ) . Based on the parameters given in this example, answer the
following questions:
1. What is the population mean (μ)? 20 minutes
2
2. What is the population variance (σ ) ? 36 minutes
3. Sketch the distribution of this population. Make sure you draw the shape of the
distribution and label the mean plus and minus three standard deviations.
1
, Problem Set 3.2: Effect Size and Power
Criterion: Explain effect size and power.
Instructions: Read each of the following three scenarios and answer the questions.
Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher
A determines that the effect size in the population of males is d = 0.36; Researcher B
determines that the effect size in the population of females is d = 0.20. All other things being
equal, which researcher has more power to detect an effect? Explain.
Researcher A, with an effect size of d = 0.36, has more power to detect an effect compared to
Researcher B with an effect size of d = 0.20. A larger effect size enhances the likelihood of
detecting true differences between groups in statistical tests, assuming similar sample sizes and
variability.
______________________________________________________________________
Two researchers make a test concerning the levels of marital satisfaction among military
families. Researcher A collects a sample of 22 married couples (n = 22); Researcher B collects
a sample of 40 married couples (n = 40). All other things being equal, which researcher has
more power to detect an effect? Explain.
Researcher B, with a larger sample size of 40 married couples, has more power to detect an
effect compared to Researcher A with a smaller sample size of 22 married couples. Increasing
the sample size increases the power of a test, allowing for a better chance of detecting true
effects or differences between groups, assuming all other factors are similar.
______________________________________________________________________
Two researchers make a test concerning standardized exam performance among senior high
school students in one of two local communities. Researcher A tests performance from the
population in the northern community, where the standard deviation of test scores is 110 (
σ 110 ); Researcher B tests performance from the population in the southern community,
where the standard deviation of test scores is 60 ( σ 60 ). All other things being equal, which
researcher has more power to detect an effect? Explain.
Researcher B, with a lower standard deviation of test scores (σ = 60), has more power to detect
an effect compared to Researcher A, with a higher standard deviation of test scores (σ = 110).
When the standard deviation is smaller, the data points are more tightly clustered around the
mean, which reduces the variability in the data. This reduced variability enhances the ability to
detect true effects or differences between groups.
______________________________________________________________________
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion: Explain the relationship between hypothesis, tests, and population mean.
Instructions: Read the following and answer the questions.
Directional versus nondirectional hypothesis testing. Cho and Abe (2013) provided a
commentary on the appropriate use of one-tailed and two-tailed tests in behavioral research. In
their discussion, they outlined the following hypothetical null and alternative hypotheses to test a
research hypothesis that males self-disclose more than females:
H0: µmales − µfemales ≤ 0
H1: µmales − µfemales > 0
2
Assessment 3 – Hypothesis, Effect Size, Power, and t
Tests
Complete the following problems within this Word document. Do not submit other files. Show
your work for problem sets that require calculations. Ensure that your answer to each problem is
clearly visible. You may want to highlight your answer or use a different type color to set it apart.
Hypothesis, Effect Size, and Power
Problem Set 3.1: Sampling Distribution of the Mean Exercise
Criterion: Interpret population mean and variance.
Instructions: Read the information below and answer the questions.
Suppose a researcher wants to learn more about the mean attention span of individuals in some
hypothetical population. The researcher cites that the attention span (the time in minutes
attending to some task) in this population is normally distributed with the following
2
characteristics: 20 36 (μ σ ) . Based on the parameters given in this example, answer the
following questions:
1. What is the population mean (μ)? 20 minutes
2
2. What is the population variance (σ ) ? 36 minutes
3. Sketch the distribution of this population. Make sure you draw the shape of the
distribution and label the mean plus and minus three standard deviations.
1
, Problem Set 3.2: Effect Size and Power
Criterion: Explain effect size and power.
Instructions: Read each of the following three scenarios and answer the questions.
Two researchers make a test concerning the effectiveness of a drug use treatment. Researcher
A determines that the effect size in the population of males is d = 0.36; Researcher B
determines that the effect size in the population of females is d = 0.20. All other things being
equal, which researcher has more power to detect an effect? Explain.
Researcher A, with an effect size of d = 0.36, has more power to detect an effect compared to
Researcher B with an effect size of d = 0.20. A larger effect size enhances the likelihood of
detecting true differences between groups in statistical tests, assuming similar sample sizes and
variability.
______________________________________________________________________
Two researchers make a test concerning the levels of marital satisfaction among military
families. Researcher A collects a sample of 22 married couples (n = 22); Researcher B collects
a sample of 40 married couples (n = 40). All other things being equal, which researcher has
more power to detect an effect? Explain.
Researcher B, with a larger sample size of 40 married couples, has more power to detect an
effect compared to Researcher A with a smaller sample size of 22 married couples. Increasing
the sample size increases the power of a test, allowing for a better chance of detecting true
effects or differences between groups, assuming all other factors are similar.
______________________________________________________________________
Two researchers make a test concerning standardized exam performance among senior high
school students in one of two local communities. Researcher A tests performance from the
population in the northern community, where the standard deviation of test scores is 110 (
σ 110 ); Researcher B tests performance from the population in the southern community,
where the standard deviation of test scores is 60 ( σ 60 ). All other things being equal, which
researcher has more power to detect an effect? Explain.
Researcher B, with a lower standard deviation of test scores (σ = 60), has more power to detect
an effect compared to Researcher A, with a higher standard deviation of test scores (σ = 110).
When the standard deviation is smaller, the data points are more tightly clustered around the
mean, which reduces the variability in the data. This reduced variability enhances the ability to
detect true effects or differences between groups.
______________________________________________________________________
Problem Set 3.3: Hypothesis, Direction, and Population Mean
Criterion: Explain the relationship between hypothesis, tests, and population mean.
Instructions: Read the following and answer the questions.
Directional versus nondirectional hypothesis testing. Cho and Abe (2013) provided a
commentary on the appropriate use of one-tailed and two-tailed tests in behavioral research. In
their discussion, they outlined the following hypothetical null and alternative hypotheses to test a
research hypothesis that males self-disclose more than females:
H0: µmales − µfemales ≤ 0
H1: µmales − µfemales > 0
2
