Question

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 $h_0$.

$h_0 : p = 0.53$
$h_1 : p \
eq 0.53$

test statistic: $z = -1.60$ $p$-value = 0.1090

\bigcirc reject $h_0$
\bigcirc there is not enough information.
\bigcirc reject $h_1$
\bigcirc do not reject $h_1$
\bigcirc do not reject $h_0$

Explanation:

Step1: Recall decision rule

For a significance test, if \( p\text{-value} < \alpha \) (significance level), reject \( H_0 \); else, do not reject \( H_0 \). Here, \( \alpha = 0.10 \), \( p\text{-value} = 0.1090 \).

Step2: Compare p - value and α

Check if \( 0.1090 < 0.10 \). Since \( 0.1090 > 0.10 \), we do not reject \( H_0 \).

Answer:

Do not reject \( H_0 \)