Students enrolled in an introductory statistics course at a university were aske
ID: 3124845 • Letter: S
Question
Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student has a visual or verbal learning style. Of the 36 students who took the survey, 22 were judged to have a visual learning style, and 14 were considered verbal learners. Consider these 36 students to be a random sample of students at this university.
Conduct a test of significance of whether these sample data provide strong evidence that more than half of all students at the university have a visual learning style. Be sure to report the hypotheses, test statistic, and p-value. Also check the technical conditions of the procedure, and write a conclusion in context.
Explanation / Answer
Formulating the null and alternatuve hypotheses,
Ho: p <= 0.5
Ha: p > 0.5 [HYPOTHESES]
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As we see, the hypothesized po = 0.5
Getting the point estimate of p, p^,
p^ = x / n = 0.611111111
Getting the standard error of p^, sp,
sp = sqrt[po (1 - po)/n] = 0.083333333
Getting the z statistic,
z = (p^ - po)/sp = 1.333333333 [TEST STATISTIC]
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As this is a 1 tailed test, then, getting the p value,
p = 0.09121122 [P VALUE]
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significance level = 0.05
As P > 0.05, we FAIL TO REJECT THE NULL HYPOTHESIS.
Hence, there is no significant evidence that more than half of all students at the university have a visual learning style at 0.05 level. [CONCLUSION]
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The problem here is that we assume that each of the trials are independent from each other. However, as the 36 participants all came from a statistics course, then they might not be independent.