Question

MAT 107 Project Serum Cholesterol Levels The table below lists the serum cholesterol levels for a sample of 30 random people. Use this data throughout the project. 193 210 196 208 188 206 240 215 201 215 199 210 242 193 208 253 288 164 214 220 194 205 223 199 206 200 204 203 240 199

11. (1 point) If someone were to ask you what the z-score for 150 means, what would you say?

12. (1 point) Construct a 95% confidence interval for the population’s mean serum cholesterol level. Assume the population standard deviation is σ = 25.0. ____________ < μ < ____________

13. (1 point) If someone were to ask you what this particular confidence interval means, what would you say?

14. Test the hypothesis that the population’s mean serum cholesterol level is greater than 200. Use α = 0.05. Assume the population standard deviation is σ = 25.0. (1 point) Alternative hypothesis (H1): ________________ (1 point) Null hypothesis (H0): _____________________ (1 point) Test statistic (z-test): ____________ (1 point) p-value: ____________

Answer 1

The given observations are -

Serum Cholesterol Levels
193
210
196
208
188
206
240
215
201
215
199
210
242
193
208
253
288
164
214
220
194
205
223
199
206
200
204
203
240
199

From these, the sample mean can be calculated as the average of these 30 observations

Sample Mean, x = 211.2

Population Standard Deviation, σ = 25

Sample Size, n = 30

Now, let us answer the questions-

11) Z-score for X=150

Z = (X-x)/σ = (150-211.2)/25= -2.45

12) 95% CI

At 95% CI, Z = 1.96

95% CI for Population Mean, M = x +- Z*σ/sqrt(n)

= 211.2 +- 1.96*25/sqrt(30)

= 211.2 +- 8.94

= (202.26, 220.14)

13) It means that there is a 95% chance that the population falls in this interval

14) population’s mean serum cholesterol level is greater than 200

H0 : M <=200

H1 : M>200

Test Statistic Z = (X-M)/σ/sqrt(n) = (211.2-200)/(25/sqrt(30)) = 2.45

P-value = P(Z>2.45) = 0.007143

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