A poll of 1000 adult Americans reveals that 48% of the voters surveyed prefer th
ID: 2908679 • Letter: A
Question
A poll of 1000 adult Americans reveals that 48% of the voters surveyed prefer the Democratic candidate for the presidency. At the 0.05 level of significance, do the data provide sufficient evidence that the percentage of voters who prefer the Democrat is less than 50%?
a) Give sampling distribution of the sample proportion (i.e what kind of distribution give the mean and standard error of the sample proportion)
b) Set up a test for the percentage of voters who prefer the democrat candidate using a significance level
c) Write a short R program to compute the P-value (Need to Use the Pnorm)
d) Assume the P value is 0.08, state your conclusion on the claim that the percentage of voters who prefer the democrat is less than 50%
Explanation / Answer
a)
Z= (p^ - p)/sqrt(pq/n)
= (p^ - 0.5)/sqrt(0.5*0.5/1000)
=(p^ - 05)/0.0158113883
b)
Ho: p = 0.50
Ha: p < 0.50
TS = (0.48 - 0.5)/0.0158113883
= -1.2649
c)
p-value = 0.10295
pnorm(-1.2649)
[1] 0.1029536
d)
since p-value > 0.05
we fail to reject the null hypothesis
there is not sufficient evidence that the percentage of voters who prefer the Democrat is less than 50%
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