1- In a random sample of 950 families living in the Camden New Jersey 247 families had annualincome below $30,000. Construct a 96% confidence interval for the proportion of families livingin Camden with income below $30,000.
2- CFO of a publicly traded company claims that the company’s average annual earnings per shareis 40 cents. To evaluate this claim, a financial analyst examines the income stamen of thecompany for the last 8 years and find the following earning per shares
59 80 -20 -5 35 40 45 50
What should be the analyst conclusion?
3- A brake shoe manufacturer claims that on the average its brake shoes last 65,000 miles. Theaverage life of a sample of 25 brake shoes was 62,3600 miles with the standard deviation of6,000 miles. Test the claim of the manufacturer.
4- Assume that life of light bulbs is normally distributed with mean 2,200 hours and standarddeviation of 140 hours.
a) What proportion of light bulbs last more than 2400 hours?
b) What proportion last between 2100 and 2300 hours?
5- A random sample of 121 college graduates is taken. Their average starting salaries is $43000with the standard deviation of $450. Construct a 98% confidence interval for population mean.
6- It is claimed that overweight individual who follow a certain diet on the average lose about 35pounds. Over an interval of 3 months a random sample of 121 overweight individuals followedthis diet. At the end of the trial the average weight loss was 33 pounds with the standarddeviation of 6 pounds. We use the following decision rule: do not reject the null hypothesis ifthe average weight loss is between 34 and 37 pounds; otherwise reject the null.
a) What is the null hypothesis?
b) Is this a 1-tailed or a 2-tailed test?
c) Given the decision rule, what is the alternative hypothesis?
d) What is the distribution of the test statistics?
e) State the critical region, acceptance region, and critical values.
f) What is your decision based on the sample information?
g) What is the probability that you made type I eror?
7- Voting turnout in a state is about 43.5%. If we take a sample of 3000 eligible voters of the state,what is the probability that more than 1350 vote?
8- Based on a study by NIH-NIAAA (National Institute of Health-National Institute on AlcoholAbuse and Alcoholism) conducted 7 years ago it was estimated that 6.2% of adult Americans are alcoholic. In a new survey of 1000 adults, 69 people were found to be alcoholic. Has the rate of alcoholism in the US changed?