Question

In: Advanced Math

Cholesterol is an established risk factor for developing heart disease. Among older age groups, men tend...

Cholesterol is an established risk factor for developing heart disease. Among older age groups, men tend to have lower cholesterol than women on average but the same is not necessarily true for younger age groups. The data provided is a sample of cholesterol levels from blood tests among university students under the age of 30. The gender of each student is also recorded.

Test whether, in this age group, there is a significant difference between the cholesterol for men and women. In particular:

State the null and alternate hypothesis
Calculate the test statistic
State the p-value (accurate to four decimal places)
Should the null hypothesis be rejected?
What do you conclude regarding the cholesterol of men and women under the age of 30?

Find a 90% confidence interval for the mean cholesterol for women under 30 using the sample provided. Show your workings and provide answers accurate to four decimal places.

Would the 90% confidence interval for the mean cholesterol for men under 30 be wider or narrower than your answer in b). Explain, without calculating the confidence interval.CholesterolGender

174	Female
177	Female
178	Female
178	Female
179	Female
180	Female
180	Female
182	Female
182	Female
182	Female
183	Female
184	Female
184	Female
185	Female
185	Female
185	Female
186	Female
187	Female
188	Female
188	Female
189	Female
189	Female
190	Female
190	Female
190	Female
191	Female
192	Female
192	Female
193	Female
193	Female
194	Female
195	Female
195	Female
195	Female
197	Female
197	Female
197	Female
197	Female
198	Female
198	Female
198	Female
199	Female
199	Female
201	Female
202	Female
174	Male
180	Male
181	Male
182	Male
186	Male
187	Male
187	Male
188	Male
188	Male
188	Male
188	Male
189	Male
189	Male
189	Male
190	Male
190	Male
191	Male
191	Male
192	Male
192	Male
193	Male
193	Male
194	Male
194	Male
194	Male
194	Male
195	Male
195	Male
196	Male
196	Male
196	Male
197	Male
198	Male
198	Male
198	Male
199	Male
199	Male
199	Male
200	Male
202	Male
203	Male
204	Male
204	Male
205	Male
207	Male

Expert Solution

Test whether, in this age group, there is a significant difference between the cholesterol for men and women. In particular:

State the null and alternate hypothesis
Calculate the test statistic
State the p-value (accurate to four decimal places)
Should the null hypothesis be rejected?
What do you conclude regarding the cholesterol of men and women under the age of 30?

Find a 90% confidence interval for the mean cholesterol for women under 30 using the sample provided. Show your workings and provide answers accurate to four decimal places.
Would the 90% confidence interval for the mean cholesterol for men under 30 be wider or narrower than your answer in b). Explain, without calculating the confidence interval.CholesterolGender

a)

i) Null Hypothesis : there is no significant difference between the cholesterol for men and women.

alternate hypothesis : there is a significant difference between the cholesterol for men and women.

H₀ :

H₁ :

ii)

Descriptive Statistics

Sample	N	Mean	StDev	SE Mean
Male	45	193.22	6.97	1.0
Female	45	189.29	7.33	1.1

test statistic

pooled std dev

Estimation for Difference

Difference	Pooled StDev
3.933	7.156

test statistic t = 2.607

degrees of freedom = 45+45-2 = 88

iii) p-value = 0.0107

iv) since p-value is less than 0.05, we reject null hypothesis

v) Since we reject null hypothesis we conclude that there is a significant difference between the cholesterol for men and women.

b) 90% CI , for one sample alpha = 0.05

90% CI for Womens data

Sample	N	Mean	StDev	SE Mean
Female	45	189.289	7.335	1.1

t_0.05,29 = 1.6802

90% CI =

90% CI = (187.4518, 191.1262)

c) Since standard deviation of Men is less than Female and the confidence level and sample size being constant the Men's will have narrower confidence interval compared to female 90% CI.

Colby Messinger answered 2 years ago

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