33(d) What would happen to the width of your interval if you were to construct a 99% CI instead(using the same survey results)?(e) Interpret theintervalyou constructed in part (c).(f)Explain what the corresponding confidencelevelmeans.(g) What (minimum) sample size would be needed for a 95% (conservative) confidence interval witha margin of error of 0.06 (or 6%)?

Cool-‐Down: Interpretations of Confidence IntervalsConsider once again the survey of American families, and recall that the 95% (conservative) confidenceinterval for the proportion of all such families that ate dinner together is given by (0.56, 0.70).Below are answers provided by students when asked to now give an interpretation of the actual 95%confidence interval computed in the study. Assess which are correct and which are not correctexplanations as to what the interval (0.56, 0.70) means (in the context of this study)?1.There is a 95% chance the confidence interval of (0.56, 0.70) will contain the true populationproportion of all families that ate dinner together last Sunday night.

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CorrectNot Correct3.If we repeated this study many times, the true proportion of all families that ate dinner together last

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34CorrectNot Correct

35

36Lab 4: Hypothesis Testing for a Population ProportionObjective:In this lab, you will learn an important statistical technique that will allow you to answer thequestion,“Was our observation due to chance, or is it more significant?” The objective is to guide youthrough the ideas behind tests of statistical significance and the statistical language involved. This labfirst presents a general overview of testing.Then, the In-‐Lab Project discusses the large sampleZ-‐test for a population proportion, as well as providing practice in answering the question of whether anevent can be attributed to chance.Application:Lucy is an Ann Arbor resident who is considering the possibility of running for a seat on theCity Council. To decide if she should invest time and money in her campaign, she wants to conduct someresearch to see if there is evidence that she could win the election (i.e. she could receive a majority of allthe votes).Overview:Hypothesis Tests:Atest of hypotheses(orsignificance test) is a procedure designed to assess what theevidence provided by the data says about some statement about a population parameter.When weconduct this hypothesis test for Lucy, we are interested in testing if the population proportion of votesthat would be cast for Lucy is greater than 0.5, ensuring her victory.Hypothesis Testing Steps:1.Determine appropriate null and alternative hypothesesand set∝.

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Term

Fall

Professor

Gunderson

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