Assignment:
There are two personality types, Type-A and Type-B. Married couples are made up of three personality-type combinations, AA, AB, and BB. Dr. Sigma Fraud, based on his pseudoanalytical theory, submitted a paper suggesting that 25% of married couples should be AA, 50% AB, and 25% BB.
Professor Panther would like to perform a scientific survey to test Dr. Fraud's theory. It turns out that Panther & Associates has already conducted a random sampling across Canada on the frequency of Type AA, AB, and BB married couples. In 145 randomly selected married couples in Canada, it is found 23 of them to be AA, 85 AB, and 37 BB.
Q1. Given the above information, what kind of hypothesis test will you conduct? Z-test, t-test, χ2-test, or F-test? Please explain.
Q2. What are the null hypothesis, the alternative hypothesis, and, hence, the "tailedness" of the test (left-tailed, right-tailed, or two-tailed)?
Q3. What is be the corresponding test statistics?
Q4. What is the resultant p-value?
Q5. What significance level should Professor Panther use if he wants to discredit Dr. Fraud's theory? And, what significance level would Dr. Fraud use in his defense, it there is any possible defense?
The following information is for Question 6 through 11.
Dr. Sehr Kurz at UMUC's Exam and Testing submitted a paper on the correlation between test scores and height in our student body. A random sample of 6 students' heights and test scores in a psychology course were used as supporting evidence. Below please find a summary of Dr. Kurz's data.
Height (in inches) 69.5 60.7 67.3 62.5 71.2 64.2
Test score 52 80 67 70 55 62
Q6. Determine the regression equation for the given data above using the equations given in Triola. Do not depend on linear regression programs to obtain your answers.
Q7. Is there a correlation between a student's height and his/her test score? What is the correlation coefficient?
Q8. If there is a correlation, is it significant at 5% or 1% significant level?
Q9. What is the explained variation?
Q10. What is the unexplained variation?
Q11. What is the total variation?