The election candidate A candidate for election believes he is supported by 60%

Question

The election candidate A candidate for election believes he is supported by 60% of the voters. He is conducting a poll of 600 randomly chosen voters to test this hypothesis. It is found that 330 of these voters support the candidate Part A Assuming that 60% of the voters support the candidate, which is the null hypothesis, what is the mean of the corresponding probability distribution for a sample size of 600? Submit My Answers Give Up Part B What is the standard deviation of the distribution in (a)? Submit My Answers Give Up Part C How many standard deviations away from the mean is 330? Submit My Answers Give Up Part D Based on the null hypothesis, calculate the probability that 330 voters or less choose the candidate. To answer this question, use a Gaussian approximation of the null hypothesis. Evaluate the probability in percent using the error function erf(t) as discussed in the lectures. The error function is tabulated below for various values of t . (Do not add the % sign in your answer-ust give the numerical answer.) 0.683 0.866 0.955 0.988 0.997 Submit My Answers Give Up Part E In the light of your previous answer, does the null hypothesis hold at a 1% significance level? O Yes 0

Explanation / Answer

Part A

Mean of the corresponding probability distributio for a sample size 600

Expected value = 600 * 0.60 = 360

Part B Standard deviation of The distribution of (A) = sqrt (0.60 * 0.40 * 600) = 12

Part C Here 330 is (330 - 360)/12 = -2.5

so it is 2.5 standard deviation away from the mean.

Part D Here we get erf(2.5 ) = 0.988

so p - value = 1 - [1/2 + erf(2.5)/2] =1 - [0.5 + 0.988/2] = 0.006

Part E

so here p- value is less than 0.01 significane level so the null hypothesis doesn't hold at 1% significance level.

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