1. The distribution of the weights of the packages received by a parcel service is normal. Nine packages are randomly selected from packages received by a parcel service. The sample has a mean weight of 15.3 pounds.
a. Find the best unbiased point estimate for the population mean weight of the packages received by the parcel service.
If the population standard deviation is 1.9 pounds and the con dence level is 95%, answer questions (b)-(d)
b. Find the critical value.
c. Find the margin of error.
d. Find a 95% con dence interval for the true mean weight, , of all packages received by the parcel service.
If the sample standard deviation is 1.9 pounds and the con dence level is 95%, answer questions (e)-(g)
e. Find the critical value.
f. Find the margin of error.
g. Find a 95% con dence interval for the true mean weight, , of all packages received by the parcel service.
2. To test the claim that the mean age of the prison population in one city is less than 26 years, a simple random sample of n = 25 is obtained from a normal population with the standard deviation = 9:2 years. The sample mean is x = 22 years. Test the claim using the signi cance level of 0.05.
a. What are H0 and H1?
b. Calculate the test statistic.
c. Find the critical value(s) for the 0.05 signi cance level.
d. What is the formula for P-value?
e. Should H0 be rejected at the 0.05 signi cance level?
f. Interpret your result.
3. The following is a simple random sample of body temperatures from 12 healthy adults. 98, 97.5, 98.6, 98.8, 98, 98.5, 98.6, 99.4, 98.4, 98.7, 98.6, 97.6
a. Are they discrete data or continuous data?
b. What is the sample mean?
c. What is the sample median?
d. What is the sample standard deviation?
e. Fill out the following frequency table
f. Based on the table above, plot the frequency histogram.
g. Based on the histogram above, is it reasonable to assume that the observations are from a normal distribution?
Assume that the observations are from a normal distribution. Use a 0.05 signi cance level to test a claim that these body temperatures come from a population with a mean that is less than 98.6oF.
h. What are H0 and H1?
i. Calculate the test statistic.
j. Find the critical values for the 0.05 signi cance level.
k. What is the formula for P-value?
l. Should H0 be rejected at the 0.05 signi cance level?
m. Interpret your result.