Original claim: the actual percentage of Americans who would vote for the incumbent president is 53%.
p = 0.53
The Null Hypothesis
H0: p = 0.53
The Alternate Hypothesis
H1: p ≠ 0.53
A sample of n = 100 has 99 degrees of freedom.
For a two tailed test and a level of significance, α = 0.1
zcritical = -1.645 and 1.645
Data:
p^= 0.45
ztest = (0.45 - 0.53) ⁄ √0.53×0.47 ⁄ 100 = -1.603
Because -1.603 is NOT in the Critical Region, we Fail to Reject the Null Hypothesis and the statistical analysis of the data can NOT reject the original claim.
Conclusion:
There is NOT sufficient evidence to warrant rejection of the claim that the actual percentage of Americans who would vote for the incumbent president is 53%.