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# LAB ACTIVITY 6: CONFIDENCE INTERVAL FOR A POPULATION PROPORTION AND POPULATION MEAN

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Author: Christine Farr
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Lab Activity 6: Confidence Interval for a Population Proportion and Population Mean1) During an election, an exit poll is taken on 600 randomly selected voters and 324 ofthose polled voted for Candidate “Jim”. A majority is needed to win the election. Weneed to construct a Confidence Interval for the Population Proportion (p) of those whovoted for Candidate “Jim” to determine whether we can declare Candidate “Jim” thelikely winner on our nightly news broadcast.The confidence interval for our population proportion is calculated:ˆˆ+/- (multiplier * SE). If the sampling distribution of is normally distributed, thenthe multiplier for the SE is the Z multiplier and the Z multiplier depends on theconfidence level we wish to have for our confidence interval.A) (5 points)Construct a 90% Confidence Interval for the population proportion of voters whowill vote for Candidate “Jim”. This work is to be done by hand, not usingsoftware.i)Test to see if we can use the normal approximation for the samplingdistribution of the sample proportion. Show all workii)If we can use the normal approximation, what is the Z multiplierˆiii)What is the SE . Show all work.iv)v)Construct your interval, show your endpoints, and then indicate thewidth of the interval by subtracting the lower endpoint from the upperendpoint. Show all work.Can we declare Candidate “Jim” the likely winner? Why or why not?B) (3 points)Using software and the above information, construct a 95% Confidence Intervalfor the population proportion of voters who will vote for Candidate “Jim”.In Minitab go to:Stat > Basic Statistics > 1 proportion >In Minitab Express go to:Statistics > 1-Sample inference > proportion (or: Inference > 1 proportion)select “summarized data”number of events = “number who voted for Candidate Jim”number of trials = “number who were polled”check “hypothesis test”ˆenter your p value in the box for the hypothesized proportionunder “options” select: confidence level = “95%”Alternative hypothesis = “proportion = hypothesized proportion”method = “normal approximation”

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