Statistics Psychology

1. A psychologist is examining the educational advantages of a preschool program and suspects that there will be significant differences in achievement based on preschool attendance. Twenty-four randomly selected 4th grade children are used in the study. Half attend a preschool program and half do not. Each child's achievement score is given below. Make sure to use the appropriate t-test for this analysis!
   Preschool: 8, 6, 8, 9, 7, 9, 6, 9, 8, 9, 7, 8
   No Preschool: 6, 5, 7, 6, 8, 5, 7, 5, 6, 7, 5, 6
   
   
   1. What is the null and alternative hypothesis (in symbols) for this t-test? (1 point)
   2. Use SPSS to calculate the appropriate t-test statistic, be sure to include your SPSS output for the t-test and descriptive statistics below. Is the t-test significant? (2 points)
   3. State your conclusion in APA format. (2 points)
2. A manager would like to know if the performance of sales representatives significantly improves over the first 6 months of employment. For 5 new sales representatives, the number of sales in the first month is recorded and the number of sales in the sixth month is recorded. The sales numbers at the 1^st and 6^th month are given below. Make sure to use the appropriate t-test for this analysis!

1. 1. What is the null and alternative hypothesis (in symbols) for this t-test? (1 point)
   2. What is the critical value for this t-test (α = .05)? (1 point)
   3. Calculate the appropriate t-test statistic (by hand) and determine if it is significant (α = .05) (2 points)
   4. State your conclusion in APA format. (1 point)
2. A researcher expects that there is a significant difference in pay for public employees in State A compared to State B. Public employees in State A are paid an average of μ = $12.50 an hour. Just over the border in State B, summary statistics on wages are not available, but a random sample of 4 public employees (This is too small of a sample, but I do not want to make this too time consuming either) are paid the wages below. Make sure to use the appropriate t-test for this analysis!
   
   $8 $8 $16 $8
   1. What is the null and alternative hypothesis (in symbols) for this t-test? (1 point)
   2. What is the critical value for this t-test (α = .05)? (1 point)
   3. Calculate the appropriate t-test statistic (by hand) and determine if it is significant (α = .05) (2 points)
   4. State your conclusion in APA format. (1 point)
      
      Is the pay for workers in State B significantly different from the pay in State A?

1. A literacy expert is trying to institute a new program for improving reading scores of people who are incarcerated. The expert finds pairs of inmates who are matched on their IQ scores and then randomly assigns one member of each pair to receive the new reading program and the other member of each pair to watch TV for the same amount of time. At the end of the program all the inmates in the study are given a reading exam. The data are:

1. 1. What is the null and alternative hypothesis (in symbols) for this t-test? (1 point)
   2. Use SPSS to calculate the appropriate t-test statistic, be sure to include your SPSS output for the t-test and descriptive statistics below. Is the t-test significant? (2 points)
   3. State your conclusion in APA format. (2 points)