develop an experimental research scenario where you could use either a one-sampl
ID: 3221856 • Letter: D
Question
develop an experimental research scenario where you could use either a one-sample or two-sample t-test or a one way analysis of variance to analyze the data and reach a conclusion about the research question posed in the example.
1. Describe an overview of the scenario and state the claim
2. identify the independent and dependent variables and at least one potentially confounding variable. state how the confounding variable(s) might be controlled.
3. state the null and alternative hypothesis in text statements and also as they would be represented with appropriate symbols.
4. describe a possible outcome in terms of the relationship between the variables in a text statement and also as it would be expressed in appropriate statistical notation
Explanation / Answer
'll give the example of how a problem can be set up and how it can be solved. Here goes:
Two-Tailed Test
Within a school district, students were randomly assigned to one of two Math teachers - Mrs. Smith and Mrs. Jones. After the assignment, Mrs. Smith had 30 students, and Mrs. Jones had 25 students.
At the end of the year, each class took the same standardized test. Mrs. Smith's students had an average test score of 78, with a standard deviation of 10; and Mrs. Jones' students had an average test score of 85, with a standard deviation of 15.
Test the hypothesis that Mrs. Smith and Mrs. Jones are equally effective teachers. Use a 0.10 level of significance. (Assume that student performance is approximately normal.)
Solution: The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
Null hypothesis: 1 - 2 = 0
Alternative hypothesis: 1 - 2 0
Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the difference between sample means is too big or if it is too small.
Formulate an analysis plan. For this analysis, the significance level is 0.10. Using sample data, we will conduct a two-sample t-test of the null hypothesis.
Analyze sample data. Using sample data, we compute the standard error (SE), degrees of freedom (DF), and the t statistic test statistic (t).
SE = sqrt[(s12/n1) + (s22/n2)]
SE = sqrt[(102/30) + (152/25] = sqrt(3.33 + 9) = sqrt(12.33) = 3.51
DF = (s12/n1 + s22/n2)2 / { [ (s12 / n1)2 / (n1 - 1) ] + [ (s22 / n2)2 / (n2 - 1) ] }
DF = (102/30 + 152/25)2 / { [ (102 / 30)2 / (29) ] + [ (152 / 25)2 / (24) ] }
DF = (3.33 + 9)2 / { [ (3.33)2 / (29) ] + [ (9)2 / (24) ] } = 152.03 / (0.382 + 3.375) = 152.03/3.757 = 40.47
t = [ (x1 - x2) - d ] / SE = [ (78 - 85) - 0 ] / 3.51 = -7/3.51 = -1.99
where s1 is the standard deviation of sample 1, s2 is the standard deviation of sample 2, n1 is the size of sample 1, n2 is the size of sample 2, x1 is the mean of sample 1, x2 is the mean of sample 2, d is the hypothesized difference between the population means, and SE is the standard error.
Since we have a two-tailed test, the P-value is the probability that a t statistic having 40 degrees of freedom is more extreme than -1.99; that is, less than -1.99 or greater than 1.99.
We use the t Distribution Calculator to find P(t < -1.99) = 0.027, and P(t > 1.99) = 0.027. Thus, the P-value = 0.027 + 0.027 = 0.054.
Interpret results. Since the P-value (0.054) is less than the significance level (0.10), we cannot accept the null hypothesis.
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