Question

# Question 11 options:

The cholesterol level of patients who had heart attacks was measured two days after the

heart attack and then again four days after the heart attack. The researchers want to see if the cholesterol level of patients who have heart attacks reduces as the time since their heart attack increases. Data is in following table:

**Cholesterol Levels (in mg/dL) of Heart Attack Patients**

**Patient**

**Cholesterol Level Day 2**

**Cholesterol Level Day 4**

1

270

218

2

236

234

3

210

214

4

142

116

5

280

200

6

272

276

7

160

146

8

220

182

9

226

238

10

242

288

11

186

190

12

266

236

13

206

244

14

318

258

15

294

240

16

282

294

17

234

220

18

224

200

19

276

220

20

282

186

21

360

352

22

310

202

23

280

218

24

278

248

25

288

278

26

288

248

27

244

270

28

236

242

Do the data show that the mean cholesterol level of patients that have had a heart attack reduces as the time increases since their heart attack? Test at the 1% level.

**if μ**

_{1}

*= mean cholesterol level of patients who had heart attacks was measured two days after the heart attack. AND**μ*_{2}

**= mean cholesterol level of patients who had heart attacks was measured four days after the heart attack. Which of the following statements correctly defines the null hypothesis**

*H*_{O}

**?**

** μ**

_{1}

**−**

*μ*_{2}

*>*0 (*μ*_{d}

*> 0)* *μ*_{1}* - μ*_{2}* *< 0 (*μ*_{d}* *< 0)

*μ*_{1}** = μ**

_{2}

*(**μ*_{d}

*= 0)***OR μ**

_{1}

*+ μ*_{2}

*= 0**Enter letter corresponding to correct answer*

** (ii) IF μ**

_{1}

*= mean cholesterol level of patients who had heart attacks was measured two days after the heart attack. AND**μ*_{2}

**= mean cholesterol level of patients who had heart attacks was measured four days after the heart attack. Which of the following statements correctly defines the alternate hypothesis**

*H*_{A}

**?**

** μ**

_{1}

**−**

*μ*_{2}

*<*0 (*μ*_{d}

*< 0)* *μ*_{1}* - μ*_{2}* *> 0 (*μ*_{d}* *> 0)

*μ*_{1}** = μ**

_{2}

*(**μ*_{d}

*= 0)*** μ**

_{1}

*+ μ*_{2}

*= 0**Enter letter corresponding to correct answer*

** **

** (iii) WHAT IS the level of significance α used:**

*Enter in decimal form. Examples of correctly entered answers: *0.01 0.02 0.05 0.10

(iv) Determine sample mean of differences xd

*Enter in decimal form to nearest hundredth. Examples of correctly entered answers: *

0.01

0.02

0.30

11.25

**(v) Determine sample standard deviation of differences s**

_{d}

*Enter in decimal form to nearest ten-thousandth. Examples of correctly entered answers: *

0.0001 0.0020 0.0500 0.3000 0.5115

* *

** (vi) Calculate and enter test statistic**

*Enter value in decimal form rounded to nearest ten-thousandth, with appropriate sign (no spaces). Examples of correctly entered answers:*

-2.0104 -0.3070 +1.6000 +11.0019

** (vii) Determine degrees of freedom for the sample of differences df**

_{d}

*:**Enter value in integer form. Examples of correctly entered answers:*

2 5 9 23 77

** (viii) Using tables, calculator, or spreadsheet: Determine and enter p-value corresponding to test statistic.**

*Enter value in decimal form rounded to nearest ten-thousandth. Examples of correctly entered answers:*

0.0001 0.0021 0.0305 0.6004 0.8143 1.0000

** **

**(ix) Comparing p-value and α value, which is the correct decision to make for this hypothesis test? **

**A. Reject H**

_{o}

**B. Fail to reject H**

_{o}

**C. Accept H**

_{o}

**D. Accept H**

_{A}

*Enter letter corresponding to correct answer.*

** **

**(x) Select the statement that most correctly interprets the result:**

**A. The result is not statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean cholesterol level of patients that have had a heart attack reduces as time increases since their heart attack. **

**B. The result is not statistically significant at .01 level of significance. There is not enough evidence to support the claim that the mean cholesterol level of patients that have had a heart attack reduces as time increases since their heart attack. **

**C. The result is statistically significant at .01 level of significance. There is not enough evidence to support the claim that the mean cholesterol level of patients that have had a heart attack reduces as time increases since their heart attack. **

**D. The result is statistically significant at .01 level of significance. Sufficient evidence exists to support the claim that the mean cholesterol level of patients that have had a heart attack reduces as time increases since their heart attack. **

*Enter letter corresponding to most correct answer*

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