# 5 Step Hypothesis Test Example

## Hypothesis Test

The alpha level denotes the level of risk at which the null hypothesis shall be rejected. Thus, setting an alpha at .05 means that the null hypothesis should be rejected if the significance level of the test is less than 5%. For instance, in testing the null hypothesis of no relationship between variables, an alpha level of .05 means that there is a 5 in 100 chance that the relationship between the variables does not exist. As such, the alpha is important in determining the statistical significance of an effect. In this case, statistical significance denotes a non-zero population effect.

**Step 1: Hypotheses**

Null hypothesis (H_{0}): the students’ mean score on attitudes about chronically mentally ill patients is equal to the mean score for people in general (µ_{students} = 75).

Alternative hypothesis (H_{A}): the students’ mean score on attitudes about chronically mentally ill patients is not equal to the mean score for people in general (µ_{students} ≠ 75).

The hypothesis test is two-sided because the direction of change in the students’ attitudes towards chronically mentally ill patients has not been specified. Thus, the alternative hypothesis is bi-directional.

**Step 2: Critical z Test Statistic**

** **The z test statistic, at the alpha level of .05, will be used to evaluate the difference in means. In this case the critical value for the two-sided test is z_{.025} = ± 1.96. In this context, the null hypothesis will be rejected if the z test statistic is greater than 1.96 or less than -1.96.

**Step 3: Calculating the z Test Statistic**

The z test statistic is calculated as follows:

**Step 4: Decision**

Since the z test statistic (z = -2.5) is less than -1.96, there is sufficient evidence against H_{0}. Therefore, the null hypothesis should be rejected.

**Step 5: Conclusion**

The students’ mean score on attitudes about chronically mentally ill patients is different from that of people in general. Thus, the film is not effective in changing the students’ attitudes about chronically mentally ill patients.

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