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.)
Submit the document to your instructor by Sunday, 11:59 p.m. central time.
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:
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What is the population mean (μ)? ____________ 20 ______________
What is the population variance ? _________ 36 _________________
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.
Researcher A has more power to detect an effect as compared to Researcher B. A large effect size means that an effect is significant. Therefore, unlike in the case of a small effect size, where the effect is unimportant, it is easier to notice an effect due to the relatively larger effect on the outcome
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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. If the Effect size is the same for both Researchers, Researcher A who has a smaller sample will have more power to detect an effect as compared to Researcher B. Ideally, if the effect size is the same, smaller sample size can detect an effect more easily as compared to large samples.
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.
Effect size is calculated by dividing the difference between the mean of the experimental group and the mean of the control group by the standard deviation ( Ialongo, 2016 ). Therefore, if the differences between the means of the experimental group and control group are the same, then the group with a larger standard deviation will have a smaller effect size. Therefore, based on the above explanation, Researcher B has more power to detect an effect as compared to Researcher A.
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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? These hypotheses represent a two-tailed non-directional test. A non-directional test entails hypotheses that predict a correlation between an independent variable, although the direction of the effect is not clearly outlined (Mourougan et al., 2017). Although the null and the alternative hypotheses describe the connection between self-discloser in males and females, it is a two-tailed test.
Do these hypotheses encompass all possibilities for the population mean? Explain.
Yes. Ideally, a null hypothesis and alternative hypothesis must incorporate all possibilities for the population mean (Mourougan et al., 2017). According to the null hypothesis, males' self-disclosure is less than or equal to female self-disclosure. On the other hand, the alternative hypothesis states that males' self-disclosure is greater than that of females. Therefore, the null and alternative hypotheses possess all possible values for the population mean.
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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.
When the p-value is less than 0.05, the null hypothesis is dismissed with the inference that the outcome probably represents the true. However, in the case where a result is marginally significant, there is a possibility of the existence of some kind of a real effect.
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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. When analyzing the population mean of education for men and women, based on the GSS Cross-Sectional Cumulative Data between 1972 and 2018, the null and the alternative hypothesis for the two variables will be:
H o : male education mean -female education mean 0
H a : male education mean – female education mean 0
References
Ialongo, C. (2016). Understanding the effect size and its measures. Biochemia medica: Biochemia medica , 26 (2), 150-163.
Mourougan, S., & Sethuraman, K. (2017). Hypothesis development and testing. IOSR Journal of Business and Management (IOSR-JBM) , 9 (5), 34-40.
