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HYPOTHESIS TESTING – PROPORTION AND ONE MEAN - SOLUTIONS

HYPOTHESIS TESTING – PROPORTION AND ONE MEAN - SOLUTIONS

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Author: Christine Farr
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Hypothesis Testing – Proportion and One Mean - SolutionsP-value Guidelines when using Standard Normal Table (i.e. the Z-table):Keep this in mind: The method for finding the p-value is based on the alternative hypothesis. Minitab will provide the p-value but if doing by hand using Table A1 observe the following:For Ha: p ≠ po then the p-value = 2P(Z ≥ |z|) That is, find 1 – P(Z < |z|) and then multiply this p-value by 2.For Ha: p > po then the p-value = P( Z ≥ z)For Ha: p < po then the p-value = P( Z ≤ z)1. A polling group surveyed a city in Scotland regarding residents’ opinions on independence from UK. It is generally believed that the percentage of ‘Yes’ votes is 50%. The poll wants to find out whether fewer than half of the residents will vote ‘Yes’. The null hypothesis is that the percentage of ‘Yes’ votes is 0.5 (50%). The alternative hypothesis is that the ‘Yes’ vote percentage is smaller than 0.5 (50%).a. Let p = true percentage of city residents who will vote ‘Yes’. Using mathematical notation, write null and alternative hypotheses about p.b. The survey polled 2000 residents, of which 1050 responded that they will vote ‘Yes’ on Scotland independence. What is the value of p-hat = percentage of ‘Yes’ votes of the sample? How does it compare to 0.5 (the general belief)?

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