 When using inferential statistics the population is defined by the researcher. 

The  Tiombe Insight Test is a psychological test designed to measure how positively a subject appraises other people.  The possible scores on the test range from 0 to 41.  During the development of the Tiombe test, it was given to several different groups of people.  Here are the results for random samples of college students from  Northern and Southern colleges.  The researchers hypothesized that  this characteristic of appraisal would differ by region.  Here are the results for by region. Group Region n Mean  s 1  North 133 25.34 5.05 2  South 162 24.94 5.44 Note: This is not a real psychological test.  Do these data support the hypothesis that Northern and Southern students differ in average measures of positive appraisal of others? (Set alpha at .05)

A confidence interval for a population mean has a margin of error of  3.4 What is the length of the confidence interval? If the sample mean is 52.8 obtain the confidence interval?    

  What null hypothesis and what alternative hypothesis should we use, if we want to test the claim that on average children attending elementary schools in a certain metropolitan area live more than 2 miles from the school which they attend?

Explain why sp    is called the pooled sample standard deviation when conducting a hypothesis test of the differences between two population means.  Why and how is the pooled sample standard deviation helpful?  

Part II (4 points each question)    

Part III (6 points each question)Please complete these problems on paper and upload at the end of the exam.

 When asked to explain why statistical significance appears so often in research reports, a student says ‘Because saying that results are significant tells us that they cannot easily be explained by chance variation or sample error alone.’  

A Community Center was interested in the effect of their program on summer loss. Summer loss is the decrease in academic knowledge from the summer to the Fall of the new year. To test their program they drew a random sample of 20 students from the program.  The students were assessed before and after the 6 week program on a 36 item assessment.  Difference scores  were calculated for the 20 students and are summarized below. (These scores were calculated by subtracting the pre test from the post test score. Each box in the chart below is a difference score for one of the 20 students. For example, the first student’s difference score is 2, the second student’s  difference score is 0, the third student’s difference score is 6.   Difference Scores on Assessment Pre-Post Program (N=20)   At  .01 significance level, do the results support the effectiveness of the program slowing summer loss? Create a 90 % confidence interval. How does the confidence interval support your decision?  

   A researcher wants to perform a hypothesis test to determine whether the mean length of marriages in California differs from the mean length of marriages in Texas.  This is a right-tailed test.