TAKE IT HOME The governor of the state of Maryland, Martin O\'Malley, ran for re

Question

TAKE IT HOME The governor of the state of Maryland, Martin O'Malley, ran for re-election in November, 2010. Before the election, from September 22-26, 2010, the Washington Post conducted a poll in which respondents were asked: "If the election for Maryland governor were held today, for whom would you vote?" 1 In an article summarizing the results of the poll, Washington Post journalists reported that "A total of 1,448 randomly selected adults in Maryland were interviewed, including... 730 voters likely to cast ballots." The sample was intended to represent the population of likely Maryland voters at that time period in September, 2010. The article summarized the responses of the likely voters using the following categories: "for Governor Martin O'Malley", "for Bob Ehrlich", and "for Other/no opinion" Although the exact counts for each response were not included in the article, the following is a likely tally of responses from the sample of 730 likely voters: for Governor Martin O'Malley for Bob Ehrlich for Other/no opinion 382 responses 302 responses 46 responses Assume that before the Washington Post conducted its poll, previous polling information had suggested the distribution of responses for the population of likely Maryland voters during this time period would be: 4896"for O'Malley", 46% "for Ehrlich", and 6% "Other/opinion". using a 2.5% significance level, perform a complete chi-square goodness-of-fit test to examine whether there was sufficient evidence to challenge the previous claim regarding the distribution of responses for the population of likely Maryland voters for that time period.

Explanation / Answer

H0 : The distribution of current responses for the population of Maryland is same as resonses for Maryland voters for the previous time period.

Ha : The distribution of current responses for the population of Maryland is differnt as responses for Maryland voters for the previous time period.

The expected responses as per the given time period.

Total number of responses = 382 + 302 + 46 = 730

For Governor Martin O ' Mailey = 730 * 0.48 = 350.4

For Bob Elrich = 730 * 0.46 = 335.8

For Other/No opinion = 730 * 0.06 = 43.8

Now the observed and expected table with chi - square statistic

X2 = (O - E)2 /E

Here X2 = 6.362

Here dF = 3 -1 = 2 and alapha = 0.025

X2critical = 7.3777

so here

X2 <   X2critical so we shalln't reject the null hypothesis and can conclude that The distribution of current responses for the population of Maryland is same as resonses for Maryland voters for the previous time period.

Responses Observed Frequency Expected (O - E)^2/E Positive 382 0.48 350.4 2.850 Negative 302 0.46 335.8 3.402 Others 46 0.06 43.8 0.111 Total 730 1 730 6.362

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