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HYPOTHESIS TESTING – PROPORTION AND ONE MEAN

HYPOTHESIS TESTING – PROPORTION AND ONE MEAN

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Author: Christine Farr
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Hypothesis Testing – Proportion and One MeanP-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. Minitabwill 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 thisp-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. Itis generally believed that the percentage of ‘Yes’ votes is 50%. The poll wants to find out whetherfewer than half of the residents will vote ‘Yes’. The null hypothesis is that the percentage of ‘Yes’ votesis 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 nulland alternative hypotheses about p.b. The survey polled 2000 residents, of which 940 responded that they will vote ‘Yes’ on Scotlandindependence.What is the value of p-hat = percentage of ‘Yes’ votes of the sample? How does it compare to 0.5 (thegeneral belief)?c. In Minitab Express use Statistics > One Sample > Proportion, click the first drop-down menuunderneath the word “Data”, and select Summarized Data. Enter 940 for “Number of events”, and 2000for “Number of trials”. Check the box that says “Perform hypothesis test”, and enter 0.50 in the boxlabeled “Hypothesized proportion:”. Click on Options and use the default 95 for “Confidence level.”Select the alternative hypothesis as “Proportion < hypothesized proportion.” Choose “Normalapproximation” for Method. Paste your output below.What value is given for the test statistic Z in the output?What is the p-value?

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