In: Statistics and Probability
Pollsters at Quinnipiac University surveyed 751 likely New York voters and found out that 368 of 751 are going to vote for Candidate A rather than Candidate B.
a)
Ho : p = 0.5
H1 : p ╪ 0.5
(Two tail test)
Level of Significance, α =
0.05
Number of Items of Interest, x =
368
Sample Size, n = 751
Sample Proportion , p̂ = x/n =
0.4900
Standard Error , SE = √( p(1-p)/n ) =
0.0182
Z Test Statistic = ( p̂-p)/SE = (
0.4900 - 0.5 ) /
0.0182 = -0.5474
p-Value = 0.5841 [excel
formula =2*NORMSDIST(z)]
Decision: p value>α ,do not reject null hypothesis
There is not enough evidence to pridicc a winner
.................
b)
z -value = Zα/2 = 1.960
[excel formula =NORMSINV(α/2)]
Standard Error , SE = √[p̂(1-p̂)/n] =
0.0182
margin of error , E = Z*SE = 1.960
* 0.0182 = 0.0358
..
c)
probability of type 1 error = 0.05
...................
d)
sample proportion , p̂ =
0.490013316
sampling error , E = 0.05
Confidence Level , CL= 0.95
alpha = 1-CL = 0.05
Z value = Zα/2 = 1.960 [excel
formula =normsinv(α/2)]
Sample Size,n = (Z / E)² * p̂ * (1-p̂) = (
1.960 / 0.05 ) ² *
0.49 * ( 1 - 0.49 ) =
384.0
so,Sample Size required=
384
..................
Please revert back in case of any doubt.
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