What is the effect on the margin of error and therefore on the accuracy of estimating a population mean by a sample mean if you increase the sample size while keeping the same confidence level?

    A random sample of 16 is selected from a normal population; mean =56 and s =12 on a selected variable.  If you are testing the null hypothesis  that the population mean = 50, what is the value of t?    

Use the attached SPSS output to answer the following questions. A researcher was interested in the differences in grades (GPA) of students who lived on campus and those who did not.   GPA 1= Residents  GPA 2= Non-Residents Do the data provide support for population differences in GPAs between the two groups? Assume α is .05.                     What statistics did you use to draw your conclusion?                     How is t constructed from other statistics on the output?    

 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.