A researcher predicts that watching a film on institutionalization will change students’ attitudes about chronically mentally ill patients. The researcher randomly selects a class of 36 students, shows them the film, and gives them a questionnaire about their attitudes. The mean score on the questionnaire for these 36 students is 70. The score for a similar class of students who did not see the film is 75. The standard deviation is 12. Using the five steps of hypothesis testing and the 5% significance level (alpha), does showing the film change students’ attitudes towards the chronically mentally ill?
What is your null hypothesis? Alternate hypothesis?
Is this a one-tailed or two-tailed hypothesis?
What is your obtained z?
What is the critical value for z?
Do you reject or fail to reject the null hypothesis?
State in words what you have found.
Answered in a previous post.
To answer these questions using hypothesis testing, we will follow the five steps outlined below:
Step 1: State the Null Hypothesis (H0) and Alternate Hypothesis (Ha):
- Null Hypothesis (H0): Showing the film does not change students' attitudes towards the chronically mentally ill.
- Alternate Hypothesis (Ha): Showing the film changes students' attitudes towards the chronically mentally ill.
Step 2: Determine the type of Hypothesis Test:
- This question does not provide a specific direction for the hypothesis (increase or decrease in attitudes), so it is a two-tailed hypothesis test.
Step 3: Set the Significance Level (alpha):
- The question states a 5% significance level (alpha = 0.05).
Step 4: Calculate the Test Statistic:
- To calculate the test statistic (obtained z), we will use the formula:
z = (sample mean - population mean) / (population standard deviation / sqrt(sample size))
Here:
- Sample mean (x̄) = 70
- Population mean (μ) = 75
- Standard deviation (σ) = 12
- Sample size (n) = 36
z = (70 - 75) / (12 / sqrt(36))
z = -5 / (12 / 6)
z = -2.5
Step 5: Determine the Critical Value and Make a Decision:
- Since this is a two-tailed test, we need to find the critical value of z for a significance level of 0.05 (two tails).
Looking up the critical values in the standard normal distribution table or using a calculator, we find:
- Critical value for alpha/2 = 0.025 is approximately ±1.96.
- Comparing the obtained z value (-2.5) with the critical value (-1.96 to +1.96):
- Since the obtained z value falls beyond the critical value range in the left tail, we can reject the null hypothesis.
Therefore, we reject the null hypothesis and conclude that showing the film does change students' attitudes toward the chronically mentally ill.