Please answer the following questions using the information below:
Below are anxiety scores for people who are taking an anxiolytic (anti-anxiety medication). These scores were taken from a random sample of 16 people. In the general population, anxiety scores are normally distributed with a mean (μ) of 25 and a standard deviation (σ) of 3. You hypothesize that this sample is not representative of the general population. Specifically, you hypothesize that these people form a distinct sub-population, with specifically LOWER anxiety, relative to the general population. That is, if they have higher anxiety, that would be treated the same as having the same amount of anxiety. Conduct a one-sample z-test by answering the following questions.
Data: 24, 26, 23, 18, 25, 19, 21, 17, 22, 26, 19, 27, 21, 22, 18 and 20
1. The null hypothesis is
2. The alternative hypothesis is
3. Are you going to be using a one- or two-tailed test?
4. Calculate your observed z-statistic.
4. Using the standard normal z-table, Find the corresponding critical z-value(s) for Type I error rate (alpha) of α = 0.05.
5. What do you conclude regarding the null hypothesis?
6. Would the p-value be greater or smaller than alpha?
7. In everyday language, what do you conclude about your research question?