This Covers 4 tests we done Since midterm So 1) The Rare Event Rule: 2) The Cent

Question

This Covers 4 tests we done Since midterm So 1) The Rare Event Rule: 2) The Central Limit Theorem 2 Props, 2 m 3) The Traditional Hypothesis Testing Method -vs- The P-value Method For each of the following hypothesis tests, write out the null and reseda hypotheses, your p-value, and give me your decision. Answer all questions. Use a 5% significance level for each test. 4) An article in the Archives of Internal Medicine reported that in a sample of 244 men, 73 had elevated total cholesterol levels (more than 200 mlgrams per deciliter). In a sample of 23 women, 44 had elevated cholesterol levels. Can you support the hypothesis that the proportion of people with elevated cholesterol levels differs between men and women? a) Repeat the above test, seeing how things differ if 60 instead if 44 women had elevated cholesterol b)

Explanation / Answer

a)

Since the picture is cut, I am assuming the total number of women to be 230

Let p1 be the proportion of men

and p2 be the proportion of women

p1 = 73/244 = 0.299

p2 = 44/230 = 0.191

n1 = 244

n2 = 230

alpha = 0.05

Null and Alternate Hypothesis:

H0: µ1- µ2 = 0 (or µ1= µ2)

Ha: µ1- µ2 > 0 (or µ1 > µ2)

Test Statistic

z = (p1-p2)/(pc*(1-pc)/n1 + pc*(1-pc)/n2)1/2

where,

pc = (n1p1+n2p2)/(n1+n2) = 0.247

z = 2.72

p-value= P(z>2.72) = 1- P(z<2.72) = 1-0.9967 = 0.0033

Result

Since, p-value < 0.05, the data is statistically significant at alpha = 0.05 and we reject the null hypothesis in favour of Alternate Hypothesis.

Conclusion

The proportion for Men is greater than Women, hence they differ.

b)

Since the picture is cut, I am assuming the total number of women to be 230

Let p1 be the proportion of men

and p2 be the proportion of women

p1 = 73/244 = 0.299

p2 = 60/230 = 0.261

n1 = 244

n2 = 230

alpha = 0.05

Null and Alternate Hypothesis:

H0: µ1- µ2 = 0 (or µ1= µ2)

Ha: µ1- µ2 > 0 (or µ1 > µ2)

Test Statistic

z = (p1-p2)/(pc*(1-pc)/n1 + pc*(1-pc)/n2)1/2

where,

pc = (n1p1+n2p2)/(n1+n2) = 0.281

z = 0.93

p-value= P(z>0.93) = 1- P(z<0.93) = 1-0.8238 = 0.1762

Result

Since, p-value > 0.05, the data is not statistically significant at alpha = 0.05 and we fail to reject the null hypothesis in favour of Alternate Hypothesis.

Conclusion

The proportion for Men is same as that of Women, hence they are equal.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.