Lab Activity 7: Hypothesis Testing for Proportions and Means: A Comprehensive Analysis Using Statistical Methods

Lab assignment covering hypothesis testing for proportions and means with statistical methods.

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Lab Activity 71Lab Activity 7Hypothesis TestingData Set: SPX MonthlyNumber of Questions: 4P-value Guidelines when using Standard Normal Table (i.e. the Z-table):Keep this in mind: The method for finding thep-value is based on thealternativehypothesis.Minitab will provideap-value but ifwe need to calculate itby hand, we would usethe StandardNormal Tableandobserve the following:i.For Ha: p < po,then the p-value = P( Zz)ii.For Ha: p > po,then thep-value = P( Zz)iii.For Ha: ppo,then the p-value = 2P(Z|z|)That is, find 1P(Z < |z|) and then multiplythis p-value by 2.1.Hypothesis Testing for aProportionExample 1Using SoftwareNo dataset is needed.Prior to the start ofaStat200 course, a survey was taken to find out students’ level of excitementfor the course. It is generally believed that 40% of all World Campus students are excited to takeelementary statistics. That means, thenullhypothesis is that the percentage of World Campusstudents excited to take elementary statistics,which wasmeasured by a “3” on the survey, is 0.40(40%). Thealternativehypothesis is that true percentage is less than 0.40 (40%).a.In this case,p= true population proportion of World Campus students who are excited to takeelementary statistics, measured by a “3” on the survey. Write the null and alternative hypothesesusing statistical notation.Hint: Remember that hypotheses are always written about thepopulation. Be sure to usenotation for the correct population parameter(should we use notation for a mean or aproportion?)!iv.Null Hypothesis:H0: P=0.40v.Alternative Hypothesis:Ha: P<0.40b.The survey for Stat200 polled 32 students, of which 10 responded that they are excited to takethe elementary statistics course.What is the value of𝑝̂= percentage of students answering “3”in thesample? Round your answer to 4 decimal places.𝑝̂= percentage of students answering “3” in thesampleis 10/32=0.3125c.How does𝑝̂in part (b) compare to the true population proportion of 0.40?Sample proportion 0.3125 is really less than the population proportion0.40.

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Lab Activity 72d.Use software to perform a hypothesis test for a proportion.Note that in this case, we do nothave a data set to follow. Instead, what we have is called “summarized data,” in other words, acount of the final values. Following the written and video instructions in the online notes forUsing Software to Perform a Summarized One Proportion Test Analysis,”use software totest the hypotheses in part (a). This is different from the instructions for the case of “raw data!”Copy and paste the output.Test and CI for One ProportionTestofp=0.4vsp<0.495%UpperSampleXNSamplepBoundZ-ValueP-Value110320.3125000.447276-1.010.156e.What value is given for the test statistic Z in the output?Z=-1.01f.What is thep-value?P-value=0.156g.One way to determine statistical significance is by using a p-value. We compare the p-value toa pre-determined significance level,α. In general, a significance level of 0.05 is used.vi.If the p-value isless thanthe significance level (0.05), werejectthe null hypothesis. Thismeans, we do not have enough evidence to claim the null hypothesis is true.vii.If the p-value isgreater thanthe significance level (0.05), wefail to rejectthe nullhypothesis. This means we do not have enough evidence to support the alternativehypothesis.Based on the p-value in part (f), do we “reject the null hypothesis” or “fail to reject the nullhypothesis?” Explain why.Wefail toreject the null hypothesis because the p value corresponding to z=-1.01 is 0.156 whichis greater than 0.05 at 5% level of significance therefore weacceptthe null hypothesis.h.In real world terms (terms of the problem), write a conclusion about the proportion of WorldCampus students who are excited to take elementary statistics.The conclusion is that the proportion of the sample who is excited isequal to 0.40theproportionof World Campus students to take the elementary statistics.i.Suppose the study intended to find out ifmorethan 40% of World Campus students are excited
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