Problems -
Problem 1 - In each diagram below, I and II represent sampling distribution of two statistics that might be used to estimate a parameter. In each case, and identify the statistic that you think would be the better estimator, or neither, and describe your choice.
Problem 2 - The U.S. Census Bureau reports the estimated mean U.S. married-couple family income is $90,835 ± $101. They describe the margin of error as providing a 90% probability that the interval defined by the estimate minus the margin of error and the estimate plus the margin of error (the lower and upper confidence bounds) contains the true value.
SOURCE: U.S. Census Bureau, 2005-2007 American Community Survey
a. What is the population and variable of interest?
b. What parameter is being estimated? What is its estimated value?
c. How is the margin of error related to the maximum error of estimate?
d. What value is being reported as the margin of error?
e. What level of confidence is being reported?
f. Find the confidence interval and state exactly what it represents.
Problem 3 - The Consumer Reports National Research Center reported that 76% of women respond, "daily or more often" when asked, "How often is your bed made?" This additional information is included as a footnote: margin of error ± 3.2 percentage points.
a. What is the population and variable of interest?
b. What parameter is being estimated? What is its estimated value?
c. What value is being reported as the margin of error?
d. Find the interval and state exactly what it represents.
e. What additional information might you want to know about this confidence interval?
Problem 4 - A recruiter estimates that if you are hired to work for her company and you put in a full week at the commissioned sales representative position she is offering, you will make "$525 plus or minus $250, 80% of the time. "She adds, "It all depends on you!"
a. What does the "$525 plus or minus $250" mean?
b. What does the "80% of the time" mean?
c. If you make $300 to the nearest $10 most weeks, will she have told you the truth? Explain.
Problem 5 - Determine the value of the confidence coefficient z(α/2) for each situation described:
a. 1 - α = 0.90
b. 1 - α = 0.95
Problem 6 - Given the information, the sampled population is normally distributed, n = 16, x- = 28.7, and σ = 6:
a. Find the 0.95 confidence interval for μ.
b. Are the assumptions satisfied? Explain.