SOLUTION: State your decision to the significance test in terms of the null hypothesis. According to a recent poll, the percentage of Americans who would vote for the incumbent president

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Question 1199454: State your decision to the significance test in terms of the null hypothesis.
According to a recent poll, the percentage of Americans who would vote for the incumbent president is 53%. If a random sample of 100 people in New York results in 45% who would vote for the incumbent, test the claim that the percentage of people in New York who would vote for the incumbent president is different from 53%. Use the following results and a 0.10 significance level to state your decision about H0.



Test statistic: z = -1.60 p-value = 0.1090
Answer by math_tutor2020(3838) About Me  (Show Source):
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Null Hypothesis = H0
Alternative Hypothesis = H1

H0: p = 0.53
H1: p =/= 0.53

In words:
Null: The percentage who voted for the incumbent was 53%
Alternative: The percentage who voted for the incumbent was NOT 53%

After doing the hypothesis test, you arrive at a p-value of roughly 0.1090
This is larger than the significance level alpha = 0.10

Recall the following rule:
If the p-value is smaller than alpha, then reject the null.
A handy phrase to remember is "If the p-value is low, then the null must go".

Since the p-value 0.1090 is NOT smaller than alpha = 0.10, we do not reject the null. We fail to reject it. We therefore "accept" the null and conclude that p = 0.53 until future evidence will overturn it.

Conclusion: 53% of American voters selected the incumbent.