Assignment:
Q1: A nationwide sample of influential Republicans and Democrats was asked as a part of a comprehensive survey whether they favored lowering environmental standards so that high-sulfur coal could be burned in coal-fired power plants. The results were:
Republicans Democrats
Number sampled 1,000 800
Number In favor 200 168
(1) State the decision rule for .02 significance level: H0: πd ≤πr H1:πd > πr
(2) Compute the value of the test statistic.
(3) Determine the p-value.
(4) Can we conclude that there is a larger proportion of Democrats in favor of lowering the standards? Use the 0.02 significance level.
Q2: The research department at the home office of New Hampshire Insurance conducts ongoing research on the causes of automobile accidents, the characteristics of the drivers, and so on. A random sample of 400 policies written on single persons revealed 120 had at least one accident in the previous three-year period. Similarly, a sample of 600 policies written on married persons revealed that 150 had been in at least one accident.
At the .05 significance level, is there a significant difference in the proportions of single and married persons having an accident during a three-year period? Determine the p-value. Hint: For the calculations, assume the single persons as the first sample.
(1) The pooled proportion is
(2) The decision rule is to reject if z is the interval
(3) The test statistic is z
(4) The p-value is .
(5) What is your decision regarding ?
Q3: Mary Jo Fitzpatrick is the Vice President for Nursing Services at St. Luke's Memorial Hospital. Recently she noticed in the job postings for nurses that those that are unionized seem to offer higher wages. She decided to investigate and gathered the following information.
Population
Group Mean Wage Standard Deviation Sample Size
Union $20.75 $2.25 40
Nonunion $19.80 $1.90 45
Would it be reasonable for her to conclude that union nurses earn more? Use the .02 significance level. What is the p-value?
(1) Is this a one-tailed or a two-tailed test?
(2) State the decision rule.
(3) Compute the value of the test statistic.
(4) What is your decision regarding HO?
(5) What is the p-value?