PSY 429 Experimental Psychology
Class Exercise #3
Hypothesis Testing with Single Sample
PSY 429 Experimental Psychology
Class Exercise #3
Hypothesis Testing with Single Sample
1. Suppose an investigator is interested in whether the mean score on an aptitude test for students who attend rural elementary schools is different from the typical score of elementary school students in general. The mean score for elementary school students in general is known to be 50. A random sample of 25 rural elementary school students is obtained, the aptitude test administered, and the mean score for the sample is found to be 56.00. The population standard deviation, s, is known to equal 10.00.
Test the null hypothesis: Ho : sample mean = population mean
2. An investigator is interested in whether the mean score on a test of short-term memory for Alzheimer's patients admitted to a private hospital is different from the mean score of Alzheimer's patients in general. The investigator believes that, in fact, the private hospital is too liberal in its criteria for diagnosing Alzheimer's Disease. Thus, he believes that he will find that the mean score for patients at the private hospital will be significantly higher than the mean score found in the general population of Alzheimer's patients (The higher the score, the stronger is short-term memory.) The mean score of typical patients diagnosed with Alzheimer's Disease is known to be 37. A random sample of 21 Alzheimer's patients at the private hospital is obtained and given the short-term memory test. The mean score for this sample is found to be 45. The standard deviation (s) of scores on this test, in general, is 6.15.
Test the experimenter's hypothesis with an alpha level set at .05.
3. Use the same experiment as described above, but with the following changes: The experimenter just wants to know if there will be a difference between his sample and the population mean.
Conduct this test with an alpha level of .01.
4. If the mean score of the population is 500 and the standard deviation of the population is 100 while the mean of a sample is 650, test the hypothesis that there is no difference between the sample mean and the population mean if the sample size is 25. Use an alpha level of .05
5. If the mean score of the population is 150 and the standard deviation of the population is 15 while the mean of a sample is 160, test the hypothesis that the sample mean will be significantly larger than the population mean if the sample size is 15. Use an alpha level of .05.
6. Test the same hypothesis and use the same data as in question #4 above except change the sample size to 45.
7.A psychologist has prepared an "optimism Test" that is administered to graduating college seniors. The test measures how each class feels about its future--the higher the score, the more optimistic the class. Last year's class had a mean score of m = 15. A sample of n = 8 seniors from this year's class was selected and tested. The scores for these seniors are listed below. On the basis of this sample, can the psychologist conclude that this year's class has a different level of optimism than last year's class?
This year's class optimism scores:7, 12, 11, 15, 7, 8, 15, 9
a. State the hypotheses and select an alpha level.
b. Determine the degrees of freedom, determine the critical values of the t statistic, and locate the critical rfegion.
c. Compute the test statistic.
d. Make a decision about the null hypothesis and state your conclusion.
8. A family therapist states that parents talk to their teenagers an average of 27 minutes per week. Surprised by that claim, a psychologist decided to collect some data on the amount of time parents spend in conversation with their teenage children. For n = 12 parents, the study revealed the following times (in minutes) devoted to conversation in a week. Do the psychologist's findings differ significantly from the therapist's claims? If so, is the family expert's claim an overestimate or underestimate of actual time spent talking to children? Use the .05 level of significance?
29, 22, 26, 22, 19, 27, 21, 24, 30, 22, 25, 28
a. State the hypothesis using symbols. Explain what they predict for this experiment.
b. Sketch the distribution and locate the critical region.
c. Calculate the test statistic.
d. Make a decision regarding the null hypothesis and state your conclusion.
9. For a standard set of discrimination problems that have been used for years in primate research, it is known that monkeys require an average of m = 20 trials before they can successfully reach the criterion (five consecutive correct solutions). A psychologist hypothesizes that the animals can learn the task vicariously, that is, simply by watching other animals perform the task. To test this hypothesis, the researcher selects a random sample of n = 4 monkeys. These animals are placed in neighboring enclosures from which they can watch another animal learn the task. After a week of viewing other animals, the four monkeys in the sample are tested on the problem. These animals require an average of 15 trials to solve the problem, with SS = 300. On the basis of these data, can the psychologist conclude that there is evidence that the animals perform significantly better after viewing others? Test the null hypothesis at the .01 level of significance.
a. State the hypothesis using symbols. Explain what they predict for this experiment.b. Sketch the distribution and locate the critical region.
c. Calculate the test statistic.
d. Make a decision regarding the null hypothesis and state your conclusion.
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