### Under what circumstances should a t distribution be used

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Question: This week's assignment questions are extracted from your Warner (2013) text. Answer each question, providing IBM SPSS analysis when necessary to support your answer.

Given below are two applications of statistics. Identify which one of these is descriptive and which is inferential. Explain your decision.

Example1: An administrator at Corinth College looks at the verbal Scholastic Aptitude Test (SAT) scores for the entire class of students admitted in the fall of 2005 (mean = 660) and the verbal SAT scores for the entire class admitted in the fall of 2004 (mean = 540) and concludes that the class of students admitted to Corinth in 2005 had higher verbal scores than the class of students admitted in 2004.

Example 2: An administrator takes a random sample of 45 Corinth College students in the fall of 2005 and asks them to self-report how often they engage in binge drinking. Members of the sample report an average of 2.1 binge drinking episodes per week. The administrator writes a report that says, "The average level of binge drinking among all Corinth College students is about 2.1 episodes per week."For what types of data would you use nonparametric versus parametric statistics?Briefly describe the difference between internal and external validity.When a researcher has an accidental or convenience sample, what kind of population can he or she try to make inferences about?For each of the following lists of scores, indicate whether the value of SS will be negative, 0, between 0 and +15, or greater than +15. (You do not need to actually calculate SS.)

Sample A: X = [103, 156, 200, 300, 98].Sample B: X = [103, 103, 103, 103, 103, 103].Sample C: X = [101, 102, 103, 102, 101].Assume that a population of thousands of people whose responses were used to develop an anxiety test had scores that were normally distributed with M = 30 and s = 10.

What proportion of people in this population would have anxiety scores within each of the following ranges of scores? Below 20.Above 30.Between 10 and 50.What is SEM?

What does the value of SEM tell you about the typical magnitude of sampling error?

As s increases, how does the size of SEM change (assuming that N stays the same)?

As N increases, how does the size of SEM change (assuming that s stays the same)?

Under what circumstances should a t distribution be used rather than the normal distribution to look up areas or probabilities associated with distances from the mean?

To complete questions 9 and 10, use the bpstudy.sav file in the Resources.Select three variables from the dataset bpstudy.sav.

Two of the variables should be good candidates for a correlation, and the other variable should be a poor candidate for a correlation. Good candidates are variables that meet the assumptions (such as normally distributed, reliably measured, interval-ratio level of measurement). Poor candidates are variables that do not meet assumptions or that have clear problems (such as restricted range, extreme outliers, gross non-normality of distribution shape).

Use the FREQUENCIES procedure to obtain a histogram and all univariate descriptive statistics for each of the three variables.

Create a scatter plot for the two "good candidate" variables.

Create a scatter plot for the "poor candidate" variable using one of the two good variables. Properly embed SPSS output where appropriate in your answer to Question 9 below. Explain which variables are good and poor candidates for a correlation analysis and give your rationale. Comment on empirical results from your data screening-both the histograms and scatter plots-as evidence that these variables meet or do not meet the basic assumptions necessary for correlation to be meaningful and honest. What other information would you want to have about the variables in order to make better informed judgments?

Is there anything that could be done (in terms of data transformations or eliminating outliers for instance) to make your poor candidate variable better?

If so, what would you recommend?

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