Question

In: Math

Complete the following problems using R. Name the file with your last name, e.g., “Prob set 6-Smith.eoc”Clearly...

Complete the following problems using R. Name the file with your last name, e.g., “Prob set 6-Smith.eoc”Clearly label problems, and be sure to turn in explanations and interpretations where appropriate.

3.Total cholesterol has been reported to be 200 mg/dL on average in the US by the Centers for Disease Control. You measure total cholesterol on a random sample of 80 Alabama adults, with the intention of comparing Alabamians’ cholesterol level to that of the US average. Data are included in the assignment .xlsx file. Assume

that cholesterol is approximately normally distributed with a known standard deviation of 70 mg/dL.

a.What is the mean value observed for Alabamians’ cholesterol?

b.What is the standard error of Alabamians’ cholesterol assuming the given known standard deviation?

c.Find the 95% confidence interval for the unknown population mean of Alabamians’ cholesterol level values and interpret its meaning.

d.Test the hypothesis that Alabamians have higher average cholesterol than that of the US at the =0.05 level. (Be sure to right down all steps, as in the lecture notes, and interpret the meaning of the test!)

e.How would your answer in (d) change if you used an =0.01 level?

116
282
213
252
150
219
221
289
226
265
234
256
208
263
155
206
201
283
208
142
279
155
231
143
218
243
162
125
212
149
250
184
210
236
241
294
196
226
184
208
278
144
263
245
212
205
208
151
266
224
276
203
222
199
272
197
176
241
269
217
206
239
238
237
187
203
283
156
283
138
234
198
172
277
172
157
267
160
243
189

Expert Solution

From the given data

a) the mean value observed for Alabamians’ cholesterol is 215.53

b.) The standard error of Alabamians’ cholesterol assuming the given known standard deviation is

Sigma / Sqrt(n) = 70 / Sqrt(80) = 7.82623

c.The 95% confidence interval for the unknown population mean of Alabamians’ cholesterol level values and interpret its meaning is

(215.53 - 1.96* 7.82623, 215.53 + 1.96* 7.82623)= (200.1906,230.8694)

d) Test the hypothesis that Alabamians have higher average cholesterol than that of the US at the =0.05 level. (Be sure to right down all steps, as in the lecture notes, and interpret the meaning of the test!)

H0: Alabamians have higher average cholesterol than that of the US is 200 mg/dL o

H1: Alabamians have higher average cholesterol than that of the US is not 200mg/dL o

Test statistic Z = (Xbar - Mu) / Standard error = (215.53 - 200) / 7.82623 = 1.98435

At alpha = 5%, Z critical values = +/- 1.96

Here Z value is not in Z critical values so we reject H0

Thus we conclude that Alabamians have higher average cholesterol than that of the US is not 200mg/dL

e). change if you used an =0.01 level then

Z critical value =+/- 2.58 at alpha = 0.01

Here Z value is in Z critical value so we accept H0

Thus we conclude that Alabamians have higher average cholesterol than that of the US is 200mg/dL

Answer: Change the conclusion

milcah answered 4 months ago

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