Statistical Hypothesis Testing
A researcher predicts that watching a film on institutionalization will change students’ attitudes about chronically mentally ill patients. The researcher randomly selects 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?
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What does it mean to set alpha at .05? Alpha at .05 means there is a .05 probability or 5% chance of committing a Type I error, which means that we have rejected our null hypothesis and found support for our alternate hypothesis when, in fact, the null hypothesis was true.
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What is your null hypothesis? Alternate hypothesis? Ho : mean of group 1 = mean of group 2 Ha : mean of group 1 ≠ mean of group 2
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Is this a one-tailed or two-tailed hypothesis? This is a two-tailed test since no direction is predicted (e.g. “will change” attitudes).
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What is the criterion z? zcrit. = -1.96 This is found by using the z table in the textbook. Since it is a two-tailed test, alpha of .05 is split between the two tails. Thus the critical z is ± 1.96, so for our example, we would use -1.96.
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Suppose the obtained z was -2.5. Do you reject or fail to reject the null hypothesis? Our obtained z value of -2.5 is more extreme (in this case smaller) than our criterionz of -1.96. We reject the null hypothesis.
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State in words what you have found. We have found that viewing the film DOES change students’ attitudes about mentally ill patients. In this case, scores were significantly lower for students who viewed the film, based on our z-test.
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What does it mean to set alpha at .05? Alpha at .05 means there is a .05 probability or 5% chance of committing a Type I error, which means that we have rejected our null hypothesis and found support for our alternate hypothesis when, in fact, the null hypothesis was true.
•
What is your null hypothesis? Alternate hypothesis? Ho : mean of group 1 = mean of group 2 Ha : mean of group 1 ≠ mean of group 2
•
Is this a one-tailed or two-tailed hypothesis? This is a two-tailed test since no direction is predicted (e.g. “will change” attitudes).
•
What is the criterion z? zcrit. = -1.96 This is found by using the z table in the textbook. Since it is a two-tailed test, alpha of .05 is split between the two tails. Thus the critical z is ± 1.96, so for our example, we would use -1.96.
•
Suppose the obtained z was -2.5. Do you reject or fail to reject the null hypothesis? Our obtained z value of -2.5 is more extreme (in this case smaller) than our criterionz of -1.96. We reject the null hypothesis.
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State in words what you have found. We have found that viewing the film DOES change students’ attitudes about mentally ill patients. In this case, scores were significantly lower for students who viewed the film, based on our z-test.