assume an assessment of the impact of the program on teachers’ productivity was
ID: 3150663 • Letter: A
Question
assume an assessment of the impact of the program on teachers’ productivity was needed. Suppose the average score among all teachers on the productivity measure was µ = 36. In the current randomly selected sample of 40 teachers, the average productivity score was 38.18. However, before a test to determine whether the program had a significant effect, there are a number of factors in need of consideration: a.) Select an appropriate alpha level. Explain this research decision (i.e., why specific value was selected) and its meaning. b.) What assumptions must be met for this test? c.) What are the two different types of errors made during a hypothesis test? How can the likelihood of each error occurring be minimized? d.) Once the statistical test has been conducted, under what conditions would the null hypothesis be rejected? How would it be determined if the null hypothesis should be rejected? e.) After conducting statistical tests, it is common practice to compute an effect size. Why is this value important?
Explanation / Answer
a) The appropriate alpha level is 0.05.
b) A standard value of alpha is used to minimize the Type I error.
c) Randomization condition: Data should be collected from a randomized survey.
10% condition: The 4o teachers are fewer than 10% of the population.
Nearly normal condition: The raw data is not provided, that is why histogram can not be drawn to check the normality condition of scores of the teachers.
d) Type I error: Rejecting a true null hypothesis.
Type II error: Failure to reject a false null hypothesis.
For minimizing the type I error, a low value of alpha need to be selected, and to minimize Type II error, alpha level has to be increased. The two Type of errors are inversely related and it is not possible to minimize both at the same time.
d) The null hypothesis might be rejected, if test statistic falls on critical region (determined based on alpha level) or a p value can be obtained and if the subsequent p value is less than alpha=0.05 (assumed significance level), reject null hypothesis.
e) Effect size has an important role in power calculation and also sample size planning.
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