#### One Sample z-Test for Proportions (Jump to: Lecture | Video )

Let's perform a one sample z-test for proportions: A survey claims that 9 out of 10 doctors recommend aspirin for their patients with headaches. To test this claim, a random sample of 100 doctors is obtained. Of these 100 doctors, 82 indicate that they recommend aspirin. Is this claim accurate? Use alpha = 0.05

Steps for One-Sample z-Test for Proportions

1. Define Null and Alternative Hypotheses

2. State Alpha

3. State Decision Rule

4. Calculate Test Statistic

5. State Results

6. State Conclusion

Let's begin.

1. Define Null and Alternative Hypotheses

 Figure 1. 2. State Alpha

Alpha = 0.05

3. State Decision Rule

Using an alpha of 0.05 with a two-tailed test, we would expect our distribution to look something like this:

 Figure 2. Here we have 0.025 in each tail. Looking up 1 - 0.025 in our z-table, we find a critical value of 1.96. Thus, our decision rule for this two-tailed test is:

If Z is less than -1.96, or greater than 1.96, reject the null hypothesis.

4. Calculate Test Statistic

 Figure 3. 5. State Results

z = -2.667

Result: Reject the null hypothesis.

6. State Conclusion

The claim that 9 out of 10 doctors recommend aspirin for their patients is not accurate, z = -2.667, p < 0.05.