Question

(a) state the hypotheses and identify the claim.
$h_0: p = 0.44$ not claim
$h_1: p \
eq 0.44$ claim
this hypothesis test is a two - tailed test.
part 2 of 5
(b) find the critical value(s). round the answer to two decimal places. if there is more than one critical value, separate them with commas.
critical value(s): -2.58, 2.58
part: 2 / 5
part 3 of 5
(c) compute the test value. round the answer to at least two decimal places.
$z = $

Explanation:

Step1: Recall z - test formula for proportion

The formula for the z - test statistic for a proportion is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$, where $\hat{p}$ is the sample proportion, $p$ is the population proportion under the null hypothesis, and $n$ is the sample size. But since the problem does not provide the values of $\hat{p}$ (sample proportion) and $n$ (sample size), we assume that maybe there was a typo or missing information in the original problem presentation. However, if we assume that this is a typical problem where, for example, if we had a sample proportion $\hat{p}$ and sample size $n$, we would substitute into the formula. But since the necessary values are not given here, we can't compute the exact value. But if we assume that this is a follow - up to a problem where, say, $\hat{p}$, $p = 0.44$ and $n$ are known, let's suppose (for illustration purposes, since the problem is incomplete) that we have $\hat{p}$, $p = 0.44$ and $n$.

Step2: Substitute values into the formula

Let's assume that we have a sample proportion $\hat{p}$ and sample size $n$. Then we calculate the standard error $SE=\sqrt{\frac{p(1 - p)}{n}}=\sqrt{\frac{0.44\times(1 - 0.44)}{n}}=\sqrt{\frac{0.44\times0.56}{n}}=\sqrt{\frac{0.2464}{n}}$. Then the z - statistic is $z=\frac{\hat{p}-0.44}{SE}$.

But since the problem as presented does not have the values of $\hat{p}$ and $n$, we can't compute the exact z - value. However, if this is a problem where, for example, in a previous part (not shown here) we had $\hat{p}=0.5$ and $n = 100$ (just for example), then $SE=\sqrt{\frac{0.44\times0.56}{100}}=\sqrt{\frac{0.2464}{100}}=\sqrt{0.002464}\approx0.0496$. Then $z=\frac{0.5 - 0.44}{0.0496}=\frac{0.06}{0.0496}\approx1.21$. But this is just an example. Since the problem is incomplete, we can't give the exact value without the necessary data.

Answer:

The problem is incomplete as the values of the sample proportion ($\hat{p}$) and sample size ($n$) are not provided. To compute the test value $z$, we need $\hat{p}$, $p = 0.44$ (from $H_0$) and $n$ to substitute into the formula $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$.