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 .1 for $p_0,$ 119 for x, and 1000 for n. Then, select $\ne p_0,$ and press enter. Doing this, we see that $z=2.002$.
Using a table of z-scores, we find that this value is more than the value of z in the table, so 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 .1 for $p_0,$ 119 for x, and 1000 for n. Then, select $\ne p_0,$ and press enter. Doing this, we see that $z=2.002$. Thus, using a table of z-values, it follows:
$P=1-.977+.023=.046$
This is less than .05, so the hypothesis is rejected.
c. We know that the value of alpha is .05. Using an error calculator, we find that the error is .021. This is more than the distance between .119 and .1, so we find that the hypothesis passes this test.
d. The hypothesis passed the third test but failed the first two tests.
