Question

(a) state the null hypothesis h0 and the alternative hypothesis h1 that you would use for the test. h0: p≥0.18 h1: p<0.18 (b) for your hypothesis test, you will use a z - test. find the values of np and n(1 - p) to confirm that a z - test can be used. (one standard is that np≥10 and n(1 - p)≥10 under the assumption that the null hypothesis is true.) here n is the sample size and p is the population proportion you are testing. np = 19.8 n(1 - p)=90.2 (c) perform a z - test and find the p - value. the value of the test statistic is given by the p - value is the area under the curve to the left of the test statistic. standard normal distribution step 1: select one - tailed or two - tailed. one - tailed two - tailed step 2: enter the test statistic. (round to 3 decimal places.) step 3: shade the area represented by the p - value.

Explanation:

Step1: Identify the type of test

The alternative hypothesis $H_1:p < 0.18$ indicates a one - tailed test.

Step2: Calculate the test statistic formula

The test statistic for a proportion is $z=\frac{\hat{p}-p}{\sqrt{\frac{p(1 - p)}{n}}}$. But we are not given $\hat{p}$ and $n$ values to calculate the test - statistic value. However, we are focused on the p - value calculation. For a one - tailed test with $H_1:p < 0.18$, we will use the standard normal distribution to find the area to the left of the test statistic.

Step3: Use the standard normal table

We need to use the standard normal (z - distribution) table to find the p - value corresponding to the calculated z - score (not given in full details here). But if we assume we have a z - score from the formula, for a left - tailed test, the p - value is the area under the standard normal curve to the left of that z - score.

Answer:

Since it is a one - tailed test with $H_1:p < 0.18$, we perform a one - tailed test. (We cannot calculate the exact p - value without the test statistic value which requires $\hat{p}$ and $n$ values not fully provided, but the nature of the test is one - tailed).