Exam 4. K300 Statistics, Prof. Kruschke. Thursday April 7, 2005, 2:30-3:45pm

Be sure to (i) write your name on every page, (ii) write clearly, (iii) show your work --an unannotated sequence of numbers that mysteriously ends up with the correct numerical answer will not be given full credit-- and (iv) answer every part of every question.

Reminder of formulas: Assuming equal variances, the t for two independent groups is

where .

A table of critical t values is displayed at the front of the room.

1. Suppose a researcher conducts an experiment with a treatment group and a control group. The scores for the groups are as follows:

Treatment Group: 27, 20, 24, 17.

Control Group: 15, 19, 11.

1A. For a non-directional hypothesis and .05 significance level, test the null hypothesis that there is zero difference between group means. Be sure to state the critical t value and your conclusion.

1B. Estimate the effect size in the population.

t-Test: Two-Sample Assuming Equal Variances

Variable 1

Variable 2

Mean

9.2

11.45

Variance

6.063157895

4.365789474

Observations

20

20

Pooled Variance

5.214473684

Hypothesized Mean Difference

0

Df

38

t Stat

-3.11585528

P(T<=t) one-tail

0.001741827

t Critical one-tail

1.685954461

P(T<=t) two-tail

0.003483653

t Critical two-tail

2.024394147

2. Suppose some data have been entered into Excel and a t test has been conducted, with output as shown at right.

2A. For a non-directional hypothesis, can we reject the null hypothesis? Why or why not?

2B. Estimate the effect size. Show your work.

3. Suppose a researcher conducts an experiment with a treatment group and a control group. The scores for the groups are as follows:

Treatment Group: 3, 20, 148, 1097 .

Control Group: 55, 403, 2981, 22026.

Which of the following transformations is best applied to the data? Explain why.

ln(x),  x^2,  sin(pi*x),  3*x-1

4. Below is shown a screenshot of the Excel resampling exercise you did in homework.

4A. Explain how the numbers in cells B4 to I4 were generated. (Give a conceptual explanation; no Excel functions are being asked for.)

4B. What is the probability that the value in cell B2 will appear in cell B4?

4C. What is the t value at the 97.5th percentile in the resampled t distribution? What is the corresponding critical t value from the usual t table? According to the resampled t distribution, is the difference of the actual-data group means significant?