Answer
a) Rejected
b) Rejected
c) Passed
d) The results are not always the same.
Work Step by Step
a) We first find the value of z using a ti-84 calculator. To do this, press "Stat," and then select "1-PropZTest." Then, plug in $p_0=0.1$, $x=119$, and $n=1000$. Then, select $\ne p_0$, and press enter. Doing this, we see that $z=2.002$.
Using a table of z-scores, we find:
$P=1−0.977+0.023=0.046$
$0.046\lt0.05$, hence we reject the hypothesis.
b)We first find the value of z using a ti-84 calculator. To do this, press "Stat," and then select "1-PropZTest." Then, plug in $p_0=0.1$, $x=119$, and $n=1000$. Then, select $\ne p_0$, and press enter. Doing this, we see that $z=2.002$.
Using a table of z-scores, we find:
$P=1−0.977+0.023=0.046$
$0.046\lt0.05$, hence we reject the hypothesis.
c) We know that the value of $\alpha=0.05$. Using an error calculator, we find that the error is $0.021$. This is more than the distance between $0.119$ and $0.1$, so we find that the hypothesis passes this test.
d) The hypothesis passed the third test but failed the first two tests.
