MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C5398C.1B59ECD0" This document is a Single File Web Page, also known as a Web Archive file. If you are seeing this message, your browser or editor doesn't support Web Archive files. Please download a browser that supports Web Archive, such as Microsoft Internet Explorer. ------=_NextPart_01C5398C.1B59ECD0 Content-Location: file:///C:/EA8CB117/Exam4preview.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" Exam 1

Exam 4. = K300 Statistics, Prof. Krusch= ke. 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 f= or 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 gr= oup. 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 hypoth= esis 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<= /p>

6.063157895

4.365789474

Observations

20

20

Pooled Variance<= /span>

5.214473684

 

Hypothesized Mean Differenc= e

0

 

Df

38

 

t Stat

-3.11585528

 

P(T<=3Dt) one-tail<= /o:p>

0.001741827

 

t Critical one-tail

1.685954461

 

P(T<=3Dt) two-tail<= /o:p>

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 follo= ws:

Treatment Group: 3, 20, 148, 1097 .

Control Group: 55, 403, 2981, 22026.<= /p>

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 ask= ed for.)

 

 

 

4B. What is the probability that the value in cell B2 w= ill appear in cell B4?

 

 

4C. What is the t value at the 97.5th percen= tile 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?

 

 

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