Author: Christine Farr


Hypothesis Testing – Proportion and One MeanUse Dataset SPXMonthlyData.P-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 thenmultiply 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 independencefrom UK. It is generally believed that the percentage of ‘Yes’ votes is 50%. The poll wants tofind out whether fewer than half of the residents will vote ‘Yes’. The null hypothesis is that thepercentage of ‘Yes’ votes is 0.5 (50%). The alternative hypothesis is that the ‘Yes’ votepercentage 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’ onScotland independence.What is the value of p-hat = percentage of ‘Yes’ votes of the sample? How does it compare to0.5 (the general belief)?c. In Minitab use Stat > Basic Stats > 1 proportion, click Summarized Data, enter 2000 fornumber of trials and 1050 for Number of events. Click on Options, AND enter 0.5 where it says“Test proportion.” Click on Options button. Use the default 95.0 for “Confidence level.” Selectthe alternative hypothesis as “Proportion < hypothesized proportion.” Choose “Normalapproximation” for Method.Minitab Express: STATISTICS>One Sample>Proportion. Under tab Data, chooseSummarized data. Then enter 1050 for number of events and 2000 for number of trials. Checkthe box to perform hypothesis test and enter 0.5 as hypothesized proportion. Then under tabOptions, choose the alternative hypothesis as Proportion< hypothesized value, use the defaultconfidence level 95 and change the method to Normal approximation. Click OK.What value is given for the test statistic Z in the output?

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