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5-Step Hypothesis Test: Z-Test

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Problem 1: Empire State College would like to know more about the age distribution of its online statistics students.
Do the data provide evidence that the mean age is not 30 years?

Problem 2: Pew Research says that 53% of American adults call themselves middle class.
The sample size was n=2413.
http://pewresearch.org/databank/dailynumber/?NumberID=559
How confident are you that between 51% and 55% of Americans call themselves middle class?
How likely is it that more than 55% call themselves middle class?

Problem 3: Some have suggested that a higher proportion of women than men under 35 use online education because they can combine online education with childcare.
Do the ESC online statistics students offer any insight into that question?
You must do a test of significance to answer this question.

Problem 4: Is there evidence that more than half the online statistics students are over 30?

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Solution Summary

The solution provides step-by-step method of performing both Z-Test for Two Samples and Z-Test for Two Proportions. All the steps of hypothesis testing (formulation of null and alternate hypotheses, selection of significance level, choosing the appropriate test-statistic, decision rule, calculation of test-statistic and conclusion) have been explained and the statistical analysis has been shown in details. Calculation of Z-Score has also been shown. Some calculations have been performed in EXCEL for better understanding.

Solution provided by:
Anwesha Ghosh, MSc
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  • MSc, Osmania University
  • MSc, Indian Institute of Technology - Roorkee (I.I.T.-ROORKEE)
  • BSc, Banaras Hindu University
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