Question

1. In the General Social Survey, an ongoing nationwide survey done by the National Opinion Research Center at the University of Chicago, a question asked is whether a respondent favors or opposes capital punishment for persons convicted of murder. The data compares the proportions who said that they were opposed to the death penalty in the year 2000 and the year 2014:

Sample:	Year:	Number who oppose the death penalty:	Sample Size:
1.	2000	337	1488
2.	2014	801	2565

Construct a 95% Confidence Interval for (p₁ – p₂) and interpret the interval.

a.) Based on the Confidence Interval, there is no significant change in the

   proportion of the population opposing capital punishment for persons

convicted of murder between the years 2000 and 2014.

b.) The proportion of the population opposing capital punishment for persons

convicted of murder was between 6% and 11% lower in 2000 than in 2014.

c.) The proportion of the population opposing capital punishment for persons

convicted of murder was between 6% and 11% higher in 2000 than in 2014.

d.) The proportion of the population opposing capital punishment for persons

convicted of murder has increased by between 2% and 8% between the

years 2000 and 2014.

e.) The proportion of the population opposing capital punishment for persons

convicted of murder has decreased by between 2% and 8% between the

years 2000 and 2014.

2. A component of cholesterol called high-density lipoprotein (HDL) is known as ‘good cholesterol’ because high levels of HDL are thought to lower the risk of coronary heart disease. It is believed that runners have increased HDL levels. The data below give details of an HDL study comparing male runners with a control group of male non-runners. At the 5% level of significance, test the claim that male runners have a higher mean HDL level than male non-runners. Assume that the populations are approximately normal.

   Runners Non-runners

   N = 40 N=45

   = 56 = 49

s = 12.1 s = 10.0

   Conduct the hypothesis test and state your conclusion.

1. p= 0.0051. Male runners do not have a higher level of HDL than male non-runners.
2. p =0.0051. Male runners do have a higher level of HDL than male non-runners.
3. p = 0.0025. Male runners do not have a higher level of HDL than male non-runners.
4. p = 0.0025. Male runners do have a higher level of HDL than male non-runners.

Answer 1

Q.1 answer: b.) The proportion of the population opposing capital punishment for persons convicted of murder was between 6% and 11% lower in 2000 than in 2014.

Explanation :

Let Proportion of the population opposing capital punishment for persons convicted of murder of the year 2014.

Proportion of the population opposing capital punishment for persons convicted of murder of the year 2000.

We want to test the hypothesis as

Let for 2014

X1 = 801 & N1 = 2565

For 2000

X2 = 337 & N2 = 1488

95% confidence interval for p1 - p2 can be calculated as follows

95% confidence interval for p1 - p2 is (0.058,0.114)

95% confidence interval doesn't contain 0. Hence Ho is rejected.

Q.2 Let be mean and standard deviation of runner

be mean and standard deviation of Non-runner

There is enough evidence to the claim that male runners have a higher mean HDL level than male non-runners.

conclusion : p = 0.0025. Male runners do have a higher level of HDL than male non-runners.

PL??