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.
Null:
Ho: µ = 75
Alternate:
Ha: µ ≠ 75
Test would be two-tailed because the alternate hypothesis does not show a specific direction (results could be in either tail of the distribution curve).
Do a z-test using the data listed in the problem.
Check a z-table for the critical values to compare to the test statistic calculated from the z-test. Use .05 level of significance for a two-tailed test to find the critical values. Compare the test statistic to the critical values from the table. If the test statistic exceeds the critical value (either tail), reject the null and conclude a change. If the test statistic does not exceed the critical value (either tail), do not reject the null (there is no difference).
I hope this will help get you started.
Assignment 2: Conducting a z-Test
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 people in general on this questionnaire is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level (i.e. alpha = .05), does showing the film change students’ attitudes towards the chronically mentally ill?
What does it mean to set alpha at .05?
What is your null hypothesis? Alternate hypothesis?
Is this a one-tailed or two-tailed hypothesis?
What is the critical z?
Calculate the obtained z. Do you reject or fail to reject the null hypothesis?
State in words what you have found.
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 people in general on this questionnaire is 75, with a standard deviation of 12. Using the five steps of hypothesis testing and the 5% significance level (i.e. alpha = .05), does showing the film change students’ attitudes towards the chronically mentally ill?
What does it mean to set alpha at .05?
What is your null hypothesis? Alternate hypothesis?
Is this a one-tailed or two-tailed hypothesis?
What is the critical z?
Calculate the obtained z. Do you reject or fail to reject the null hypothesis?
State in words what you have found
To determine if showing the film changes students' attitudes towards the chronically mentally ill, we can use hypothesis testing. Here's how we can approach this problem using the five steps of hypothesis testing:
1. Null hypothesis: The null hypothesis (H0) states that there is no change in students' attitudes towards the chronically mentally ill after watching the film. In this case, the null hypothesis would be: The mean score on the questionnaire for students who watch the film is the same as the mean score for students who did not watch the film. Therefore, in statistical terms, H0: μ = 75.
2. Alternative hypothesis: The alternative hypothesis (H1) states that there is a change in students' attitudes towards the chronically mentally ill after watching the film. In this case, the alternative hypothesis would be: The mean score on the questionnaire for students who watch the film is different from the mean score for students who did not watch the film. Therefore, in statistical terms, H1: μ ≠ 75.
3. Hypothesis type: Since the alternative hypothesis states that there is a change in attitudes (either an increase or a decrease) as a result of watching the film, this is known as a two-tailed hypothesis.
4. Obtained z-score: To calculate the obtained z-score, we need to use the formula: z = (x̄ - μ) / (σ / √n), where x̄ is the sample mean, μ is the population mean (which is given as 75), σ is the standard deviation (which is given as 12), and n is the sample size (which is 36). Plugging in these values, we get: z = (70 - 75) / (12 / √36) = -5 / (12 / 6) = -5 / 2 = -2.5.
5. Critical value for z: Since the significance level (alpha) is 5%, or 0.05, and this is a two-tailed test, we need to divide the alpha level by 2 to get the critical value in each tail. Utilizing a standard normal distribution table, the critical value for each tail (with alpha/2 = 0.05/2 = 0.025) is approximately ±1.96.
Now, we compare the obtained z-score (-2.5) with the critical value (-1.96 and 1.96). Since -2.5 falls in the rejection region (outside the range of -1.96 to 1.96), we can reject the null hypothesis.
In conclusion, based on the hypothesis test, we reject the null hypothesis. This suggests that showing the film does change students' attitudes towards the chronically mentally ill, although we cannot determine from this test alone whether the change is positive or negative.