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 of color to set it apart.)
Problem Set 5.1: 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 characteristics: 20 36 . Based on the parameters given in this example, answer the following questions:
- What is the population mean (μ)?
- What is the population variance ?
- Sketch the distribution of this population. Make sure you draw the shape of the distribution and label s the mean plus and minus three standard deviations.
Problem Set 5.2: 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. __________________________________________________________
- 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. _____________
- 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 ( ); Researcher B tests performance from the population in the southern community, where the standard deviation of test scores is 60 ( ). All other things being equal, which researcher has more power to detect an effect? Explain. __________________________________________________________
Problem Set 5.3: Hypothesis, Direction, and Population Mean
Criterion: Explain the relationship between hypothesis, tests, and population mean.
Instructions: Read the following and answer the question.
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
- What type of test is set up with these hypotheses, a directional test or a nondirectional test? ______________________________________________________
- Do these hypotheses encompass all possibilities for the population mean? Explain. __________________________________________________________
Problem Set 5.4: Hypothesis, Direction, and Population Mean
Criterion: Explain decisions for p values.
Instructions: Read the following and respond to the prompt.
The value of a p value. In a critical commentary on the use of significance testing, Lambdin (2012) explained, “If a p < .05 result is ‘significant,’ then a p = .067 result is not ‘marginally significant’” (p. 76). Explain what the author is referring to in terms of the two decisions that a researcher can make. ________________________________________________________________
Problem Set 5.5: Create Your Hypothesis
Criterion: Create a hypothesis and a null hypothesis for a research project.
Instructions: Write a hypothesis and a null hypothesis for the two variables you downloaded from GSS. This hypothesis and null hypothesis will be part of your final project.
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