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1. A mayoral election race is tightly contested. In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor. Based on this sample, what is the initial hunch? Would one claim with 95% confidence that the mayor will win a majority of the votes? Explain.

2. As a sample size approaches infinity, how does the student's t distribution compare to the normal z distribution? When a researcher draws a sample from a normal distribution, what can one conclude about the sample distribution? Explain.

https://brainmass.com/statistics/normal-distribution/statistics-238997

#### Solution Preview

(1) 572/1100 = 0.52. It appears that the election is tightly contested.

p = 0.52, q = 1 - p = 0.48

Standard error, SE = sqrt(pq/n) = sqrt(0.52 * 0.48/1100) = 0.0151

H0: p = 0.5 and Ha: p > 0.5

z = (p - p')/SE

z = (0.52 - 0.5)/0.0151 = 1.3245

P(z > 1.3245) = 0.093

Since 0.093 > 0.05, we can not say with 95% confidence that the mayor will win a majority of votes.

(2) A careful look into ...

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