Need to complete the assignment
Introduction to Statistical Modeling
Case Assignment 3
Chapter 9
Instructions:
Show ALL your work manually. That means that all calculations must be shown in their entirety. You must use the formulae used in the textbook. You can add extra space as needed for your answers. You must include the Honor Pledge on all your assignments.
A toaster manufacturer receives large shipments of thermal switches from a supplier. A sample from each shipment is selected and tested. The manufacturer is willing to send the shipment back if the proportion of defective switches is more than 5%. Otherwise, the shipment will be kept.
State the appropriate null and alternative hypotheses to be tested by the manufacturer.
H0:
H1:Describe the Type I error.
Describe the Type II error for this problem.
From the manufacturer's point of view, which error would be the more serious?
Justify your answer.
From the supplier's point of view, which error would be the more serious?
Justify your answer.
Develop the null and appropriate hypotheses that are most appropriate for each of the following situations:
A meteorologist claims that the average high temperature for the month of August in Chicago, Illinois is 83°F. If the residents of Chicago do not believe this to be true, what hypotheses should they test?
H0: ______________
H1: ______________
A car manufacturing plant is acting in accordance with the public's interest in making cars that have gas mileage of at least 28 miles per gallon. The supervisor will only let the cars off the manufacturing floor if the gas mileage is more than 28 miles per gallon. What hypotheses should the plant test?
H0: ______________
H1: ______________
A spokesperson for the Health Department reports that a fish is unsafe for human consumption if the polychlorinated biphenyl (PCB) concentration exceeds 5 ppb. The Carlson family is interested in the mean PCB concentration in a fish from the lake on which they live. What hypotheses should they test?
H0: ______________
H1: ______________
An Internet survey revealed that 50% of Internet users received more than 10 e-mail messages per day. A similar study on the use of e-mail was repeated. The purpose of the study was to see whether use of e-mail has increased.
H0: ______________
H1: ______________
The Iowa Department of Transportation repaired hundreds of bridges in 1993. To check the average cost to repair a bridge, a random sample of n = 55 bridges was chosen. The mean and standard deviation for the sample are $25,788 and $1,540, respectively. Records from previous years indicate an average bridge repair cost was $25,003. Use the sample data to test that the 1993 mean
is greater than $25,003. Use 
= 0.05.Test statistic =
Critical Value(s) =
Conclusion:
A new light bulb is being considered for use in an office with computers. It is decided that the new bulb will only be used if it has a mean lifetime of more than 500 hours. A random sample of 40 bulbs is selected and placed on life test. The mean and standard deviation are found to be 505 hours and 18 hours, respectively. Perform the appropriate test of hypothesis to determine whether the new bulb should be used. Use a 0.01 level of significance.
Test statistic =
Critical Value(s) =
Conclusion:
The manufacturer of a particular battery pack for laptop computers claims its battery pack can function for 8 hours, on the average, before having to be recharged. A random sample of 36 battery packs was selected and tested. The mean functioning time before having to be recharged was 7.2 hours with a standard deviation of 1.9 hours. A competitor claims that the manufacturer's claim is too high. Perform the appropriate test of hypothesis to determine whether the competitor is correct. Test using
= 0.05.Test statistic =
Critical Value(s) =
Conclusion:
Interpretation:
Find the p-value for this test.
An airline company would like to know if the average number of passengers on a flight in November is less than the average number of passengers on a flight in December. The results of random sampling are printed below.
Test the appropriate hypotheses using
= 0.01.
Test statistic =
Critical Value(s) =
Conclusion:
Interpretation:
In testing the hypotheses H0: p1 - p2 = 0 vs. Ha: p1 - p2 > 0, use the following statistics, where x1 and x2 represent the number of defective components found in medical instruments in the two samples.
n1 = 200, x1 = 80
n2 = 400, x2 = 140
What conclusion can we draw at the 5% significance level?
Test statistic =
Critical Value(s) =
Conclusion:
What is the p-value of the test?
p-value =
Explain how to use the p-value to test the hypotheses.
Estimate with 95% confidence the difference between the two population proportions.
