Here is the screenshot of the basic StatCrunch solution.

[My **Excel** calculator for running this test is found here.]

As always for proportion problems, we have to check first to be sure n*p and n*q or n*(1-p) are both > 5.

If they are, we can use the normal approximation to the binomial (a proportion is essentially a binomial test). That is why f**or all the proportion problems we do in this course we use the z-test**. If either n*p or n*q is not > 5, we have to use a test that is beyond the scope of this course.

Step 1 as almost always is true for us, is to click on **Stat** once StatCrunch is open. The sequence is **Stat>Proportion Stats>One Sample>With Summary**. Then enter the number of success, which is just n*p, the sample size, select the Hypothesis test for p, and enter the null hypothesis and select the math operator for Ha. Click **Compute!** The answer window opens and you can see the test statistic of z= -1.042 and the p-value of 0.29. Although this problem asks us to find the critical value and make our decision based on that, the p-value always agrees and tells us we Fail to Reject the null since p>α.

I used the **Stat>Calculators>Normal** path to bring up the normal calculator. Because this is a two-tailed test (recall Ha has the ≠ math operator), I like to use the **Between** button and enter the confidence level c, which is 1-α or 0.9. The calculator shows the two critical values and rejection areas. Because the test statistic of -1.042 does not fall in either rejection area, we get the same decision of **Fail to Reject the null**.

The final part is to draw a conclusion. Recall the alternative was the claim, so we say: **Fail to Reject Ho. The data do NOT provide sufficient evidence to Support the claim.**

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