t-tests Directions: Write the null and alternate hypothesis, determine the appropriate t-test for each of the following problems, decide upon a decision rule, draw the rejection region, and write a statement that describes the relationship the researcher is entitled to make. (You may use Excel to calculate means, variance and standard deviation). 1. An investigator predicts that individuals that fit the Type A Behavior Pattern (highly competitive and time conscious) will have higher scores on a questionnaire measure of need for achievement that individuals that fit the Type B Behavior pattern (absence of Type qualities). The investigator collects need for achievement scores from 10 Type A subjects and 10 Type B subjects. Higher scores reflect greater levels of need for achievement. Type A Type B 12 102. An investigator believes that families in Virginia have more children on average than the average number of children in the population of the United States. From census data the investigator knows that he mean number of children in the LLB. is 2.1 children. She draws a sample of seven families Jfrom the state of Virginia and obtains the number of children for each family. The data from this sample are presented below. Write the null and alternative hypotheses for testing the investigator's prediction. Scores for the seven families: 3, ti. 2. t], 4, 6, T 3. An investigator conducts a study to examine the benefits of psychotherapy for individuals with depression. Specifically, the investigator predicts that depressed individuals who receive psychotherapy in addition to drug therapy for depression will display significantly lower levels of depression than persons with a diagnosis of depression who receive only drug therapy. The investigator assigns 10 subjects to each of the two groups stated above. After three months the investigator measures depression using a scale in which higher scores reflect higher levels of depression. Psychotherapy plus drug therapy group: 23, 19, 16, 18, 15, 22, 16, 18, 19, 20 Drug therapy only: 24, 27, 26, 28, 29, 24, 26, 25, 22, 28