Probability and Statistics – Mrs. Leahy
Unit 8 Homework Problems
Section 1: Estimating µ when σ is known
COMPLETE THE FOLLOWING ON YOUR OWN PAPER
1. Allen’s hummingbird (Selasphorussasin) has been studied by zoologist Bill Alther. A small group of 15 Allen’s hummingbirds has been under study in Arizona. The average weight of these birds is grams. Based on previous studies, we can assume that the weight of Allen’s hummingbirds have a normal distribution, with σ =0.33 grams.
a) Find an 80% confidence interval for the average weights of Allen’s hummingbirds in the study region. What is the margin of error (E)?
b) What conditions are necessary for your results?
“The x distribution is normal” or “The sample size is ≥ 30”
c) Give an interpretation of your results. We can conclude that…. etc
2. Total plasma volume is important in determining the required plasma component in blood replacement therapy for a person undergoing surgery. Plasma volume is influenced by the overall health and physical activity of an individual. Suppose that a random sample of 45 male firefighters are tested and that they have a plasma volume sample mean of . Assume that σ=7.50 ml/kg for the distribution of blood plasma.
a) Find a 99% confidence interval for the population mean blood plasma volume in male firefighters. What is the margin of error (E)?
b) What conditions are necessary for your results?
“The x distribution is normal” or “The sample size is ≥ 30”
c) Give an interpretation of your results. We can conclude that…. etc
3. Thirty small communities in Connecticut (population near 10,000 each) gave an average of reported cases of larceny per year. Assume that σ is known to be 42.6 cases per year.
a) Find a 90% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
b) Find a 95% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
c) Find a 99% confidence interval for the population mean annual number of reported larceny cases in such communities. What is the margin of error?
d) Compare the margins of error for parts (a) to (c). As the confidence levels increase, what happens to the margins of errors?
e) Compare the LENGTHS of the confidence intervals for parts (a) to (c). As the confidence levels increase, what happens to the length of the confidence intervals?
Answer TRUE or FALSE:
4. The value is a value from the standard normal distribution such that .
5. The point estimate for the population mean µ of an x distribution is , computed from a random sample of the x distribution.
6. Consider a random sample of size n from an x distribution. For such a sample, the margin of error for estimating µ is the magnitude of the difference between and µ.
7. Every random sample of the same size from a given population will produce the exact same confidence interval for µ.
8. A larger sample size produces a longer confidents interval for µ.
9. If the standard deviation for an x distribution decreases, c confidence intervals based on the same sample size will become shorter.
10. If the sample mean of a random sample from an x distribution is relatively small, then the confidence interval for µ will be relatively short.
11. For the same random sample, when the confidence level c is reduced, the confidence interval for becomes shorter.
Section 2: Estimating µ when σ is unknown
COMPLETE THE FOLLOWING ON YOUR OWN PAPER
Note: Use the information from part a), but you do not have to verify the information using a calculator.
1.
2.
3.
Section 3: ESTIMATING p
Use your yellow textbook to do the following
pg 456-457 #11,12,16, 17, 23, 34