4. A famous logic problem has four possible answers (A, B, C, and D). Extensive study has demonstrated that ...

1. A goodness-of-fit test involves three different categories.
a. How many degrees of freedom are associated with this test?
b. What is the critical value for χ2 at α=.05?
c. What is the critical value at α=.01?

2. 6. If a test is reliable, each subject will tend to get the same score each time he or she takes the test. Therefore, the correlation between two administrations of the test should be high. The reliability of the verbal GRE was tested using five subjects, as shown in the table below:
verbal GRE (1) verbal GRE (2)
540 570
510 520
580 600
550 530
520 520
a. What is the value of the correlation coefficient? What is the value of SP (sum of the products – numerator of the correlation coefficient)? What is the value of SSx and SSy ?
b. Is the correlation significantly different from zero? what is the critical r value?
c. calculate the regression line predicting the second exam from the first exam. What is the value of the slope what is the value of the Y intercept
d. Does the slope provide support for a significant linear relationship between exam 1 and exam 2?
SS regression =
df regression=
MS regression =
SS residual =
df residual=
F=?(1pt)
SS total=
What is the critical F value?
What is your statistical decision? 

3. 8. In spite of what may seem obvious, medical research has shown that being cold is not related to catching a cold. Imagine that in one such study, 40 subjects were exposed to cold viruses. Then half of the subjects were randomly assigned to remain in a cold room for several hours, and the other half remain in a room kept at ordinary room temperature. At the end of the experiment, the numbers of subjects who catch a cold are as shown in the following table:
cold room normal temperature room Total
caught cold 14 12
no cold 6 8
Total
a. What is the null hypothesis? Being cold is not related to catching a cold.
b. test the null hypothesis at the .05 level. What is the value of the critical value? What is the value of the test statistic (show work)? What is your conclusion?
c. given your decision, which type of error (type I or II) could you be making ?

4. A famous logic problem has four possible answers (A, B, C, and D). Extensive study has demonstrated that 40% of the population chooses the correct answer A, 26% choose B, 20% choose C, and 14% choose D. A new study has been conducted with 50 subjects to determine whether presenting the problem in concrete terms changes the way subjects solve the problem. In the new study, 24 subjects choose A, 8 subjects choose B, 16 subjects choose C, and only 2 subjects choose D.
a. State the null and alternative hypotheses
b. Calculate the appropriate test statistic .
c. How many degrees of freedom are there for this test statistic?
d. What is the critical value for alpha = .05 ?
e. State your conclusions in terms of the original research question

5. Suppose there is a perfect negative correlation between the amounts of time spent (on average) answering each question on a test and the total score on the test. Assume that Mx=30 seconds, and sx=10 seconds for the time per item, and that My=70, with Sy=14 for the total score.
a. If someone spent 10 seconds per item, what total score would they receive?
b. If someone’s score on the exam was 49, how many seconds did they spend per item?