Lab Activity 7: Hypothesis Testing for Proportions and Means: A Comprehensive Analysis Using 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( Z≤z)ii.For Ha: p > po,then thep-value = P( Z≥z)iii.For Ha: p≠po,then the p-value = 2P(Z≥|z|)That is, find 1–P(Z < |z|) and then multiplythis p-value by 2.1.Hypothesis Testing for aProportion–Example 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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