Parameter Estimation and Confidence Intervals1. A marriage counselor applies the Global Distress Scale (GDS) which measures global marital
discord.
global marital discord. This scale consists of 43 true/false questions with a total score of
true/false questions with a combined total score for the two spouses
(Snyder, Willis, & Grady-Fletcher, 1991). She asks you to provide a rough estimate of the
average
rough estimate of the average score of your clientele. You obtain a random sample of 125
couples
a random sample of 125 couples and determine a mean EAG score of 59 points on the EAG
scale with
59 points on the EAG scale with a standard deviation of 5.2. Following the
procedure provide a 95% confidence interval of the mean EAG score of the clients in the
EAG mean EAG score of the counselor’s clients.
2. You need to compute an interval of the mean ages of voting-age adults in a constituency for
a
voting-age adults in an electoral district, for this you obtain a random sample of 272 voting-age
adults and
272 voting-age adults and determines a mean age of 36.3 years with a standard deviation of 9.7
years.
a standard deviation of 9.7 years. Develop a 99% confidence interval.
3. The American Restaurant Association collected information on the number of times
times young married couples eat out per week. A
A survey of 60 couples indicated that the average number of meals away from home
2.76 meals per week, with a standard deviation of 0.75, also per week.
per week. Construct the 97% confidence interval of the population mean.
population mean.
4. During a national debate on changes in the health care system, a cable news service
conducted a survey of the
cable news service conducted an opinion poll of 500 small business owners.
business owners. It was revealed that 65% of these small business owners
do not approve of the changes. Construct the 95% confidence interval of the proportion
opposed to the changes.
of the proportion who oppose such changes in the health care system. Comment on the
results.
5. Near the election, a cable news service conducts an opinion poll of 1, 000 likely voters.
survey of 1,000 likely voters. The result shows that the
Republican challenger has a 52 percent to 48 percent lead.
a. Construct the 95 percent confidence interval of the proportion favoring
the Republican candidate.
b. Calculate the probability that the Democratic candidate is the actual frontrunner.
c. Repeat the above analysis based on a sample of 3,000 likely voters.
voters.
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