Hypothesis Testing Chapter 9
Textbook Problems: 20,26,30 (Show all your work and discuss your responses)
20. The Disk Brake Case
National Motors has equipped the ZX-900 with a new disk brake system. We define u to be the mean stopping distance (from a speed of 35mph) of all ZX-900s. National Motors would like to claim that the ZX-900 achieves a shorter mean stopping distance than the 60ft claimed by a competitor.
a. Set up the null and alternative hypotheses needed to support National Motor’s claim.
b. A television network will allow National Motors to advertise its claim if the appropriate null hypothesis can be rejected a = .05. If a random sample of 81 ZX-900’s have a mean stopping distance of 57.8 ft, will National Motors be allowed to advertise the claim? Assume that the population standard deviation equals 6.02 ft and justify your answer using both a critical value and p-value.
26. Air Safety Case
Recall that it is hoped that the mean alert time, u, using the new display panel is less than eight seconds.
(1)
Formulate the null hypothesis Ho and the alternative hypothesis Ha that would be used to attempt to provide evidence that u is less than eight seconds
(2)
Discuss the meanings of a Type I error and a Type II error in this situation.
(3)
The mean and the standard deviation of the sample of 15 alert times are 7.4 and 1.0261, respectively. Test Ho vs. Ha by setting a equal to .05 and using a critical value. Assume that the population of alert times using the new display panel is approximately normally distributed.
(4)
Interpret the p-value of .02 for the test.
30. The Bank Customer Waiting Time Case
Recall that a bank manager has developed a new system to reduce the time customers spend waiting for teller service during peak hours. The manager hopes the new system will reduce waiting times from the current 9 to 10 minutes to less than 6 minutes.
a. Letting u represent the mean waiting time under the new system, set up the null and alternative hypothesis needed if we wish to attempt to provide evidence supporting the claim that u is shorter than 6 minutes.
b. The mean and standard deviation of a sample of 100 bank customer waiting times are 5.46 and 2.475 respectively.
(1)
Use a critical value to test the hypotheses you set up in part a by setting a equal to .05
(2)
Interpret the p-value of .0158 for the test.
Other Problems: In addition to hypothesis testing include the type I and Type II errors.
A. GM wants to test a new catalytic converter to determine whether it meets new air pollution standards. The mean emission of all converters of this type must be less than 20 parts per million of carbon. Ten (10) converters are manufactured for testing purposes and their emission levels are measured, with a mean of 17.17 and a standard deviation of 2.98. Test the hypotheses at a = .01. Show work and discuss.
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B. WeDo carpet company advertises that it will deliver your carpet within 15 days of purchase. A sample of 49 past customers is taken. The average delivery time in the sample was 16.2 days. Assume the population standard deviation is known to be 5.6 days.
a. |
State the null and alternative hypotheses. |
b. |
Using a critical value, test the null hypothesis at the 5% level of significance. |
c. |
Using a
p-value, test the hypothesis at the 5% level of significance. |
d. |
What type of error may have been committed for this hypothesis test? Why? |
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C. A radio show in main street usa has complained that the average monthly rent for an efficiency apartment in that city is $600 or more. The main street association believes that this claim is an exaggeration. Main street takes a random sample of 100 efficiency apartments in the city, inquiring about the monthly rent charged for each. The mean rent for the 100-apartment sample is $592. Conduct a hypothesis test with
?
= .05 and draw your conclusion using the
p-value approach. (Assume the standard deviation for all efficiency apartment rents in this city is known to be about $52.)
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D. From a population of cans of coffee marked "12 ounces," a sample of 50 cans was selected and the contents of each can were weighed. The sample revealed a mean of 11.8 ounces with a standard deviation of 0.5 ounces.
a. |
Formulate the hypotheses to test to see if the mean of the population is at least 12 ounces. |
b. |
Compute the test statistic. |
c. |
Using the
p-value approach, what is your conclusion? Let a = .05. |
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E. The average starting salary of students who graduated from colleges of Business in 2014 was $48,400. A sample of 100 graduates of
2015
showed an average starting salary of $50,000. Assume the standard deviation of the population is known to be $8,000. We want to determine whether or not there has been a significant
increase
in the starting salaries.
a. |
State the null and alternative hypotheses to be tested. |
b. |
Compute the test statistic. |
c.
|
The null hypothesis is to be tested at 95% confidence. Determine the critical value for this test. |
d. |
What do you conclude? |
e. |
Compute the p-value. Discuss. |
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Chapter 12
Textbook Problems: 20,28 (Show your work and discuss your responses)20. In the book
Essentials of Marketing Research,William R. Dillon, Thomas J. Madden and Neil A. Firtle discuss the relationship between delivery time and computer-assisted ordering. A sample of 40 firms shows that 16 use computer-assisted ordering, while 24 do not. Furthermore, past data are used to categorize each firm’s delivery times as below the industry average, equal to the industry average, or above the industry average. The results obtained are given in table 12.6.
a. Test the hypothesis that the delivery time performance is independent of whether computer-assisted ordering is used. What do you conclude by setting a =.05?
b. Verify that a chi-square test is appropriate.
c. Is there a difference between delivery-time performance between firms using computer-assisted ordering and those not using computer-assisted ordering?
d. Carry out Graphical analysis to investigate the relationship between delivery-time performance and computer-assisted ordering. Describe the relationship.
Table 12.6
Delivery Time |
Computer |
Below |
Equal to |
Above |
Assited |
Industry |
Industry |
Industry |
Row |
Ordering |
Average |
Average |
Average |
Total |
No |
4 |
12 |
8 |
24 |
Yes |
10 |
4 |
2 |
16 |
Column Total |
14 |
16 |
10 |
40 |
Other Problems:
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A. A study of car accidents and drivers who use cell phones collects the following sample data.
Use a significance level of 0.05 and determine if the use of a cell phone and having an auto accident are independent. (Null hypothesis is that they are independent.)
|
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B. Five hundred randomly selected automobile owners were questioned on the main reason they had purchased their current automobile. The results are given below.
Styling
|
Engineering
|
Fuel Economy
|
Total
|
Male |
70 |
130 |
150 |
350 |
Female |
30 |
20 |
100 |
150 |
Total |
100 |
150 |
250 |
500 |
a. |
State the null and alternative hypotheses for a contingency table test. |
b. |
State the decision rule for the critical value approach. Let a = .01. |
c. |
Calculate the test statistic. |
d. Discuss your conclusion for this test.
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C. Consider a set of 50 measurements with mean 50.2 and standard deviation 18.7 and with the following observed and expected frequencies.
It is desired to test whether these measurements came from a normal population. At a significance level of .05, test
H
0: the set of 50 measurements came from a normal population.Accept or reject Null and show work with chi square.
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Linear Regression Chapters 13 & 14:Use the descriptive statics excel add on tool pack for regression and easier solving. NOTE: Excel fo A. & B. will be attached.Textbook Chapter 13 Problems: 16,18,26 & the following two other problems:Other Problems:Run the regression model for the following two Excel problems and answer the questions under methods and applications on page
483-484 parts a thru j (Attached)You can use the descriptive statistics excel add on tool pack for regression for easier solving to get the output. Here it is important to discuss each of those areas and outputs. Since excel does most of the work here, it is important that you provide your opinions and comments for full credit.
Attached
A. Excel Data Set 1: SalesAdv
B. Excel Data Set 2: StockRtn
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Textbook Chapter 14 Problems: 16, 18, 24 & the following three other problems:Questions in separate attachment
Other Problems:Run the regression model for the following three Excel problems and answer the questions under methods and applications on
page 540 (7 steps).You can use the descriptive statistics excel add on tool pack for regression and easier solving to get the output. Here it is important to discuss the each of those areas and outputs. Since excel does most of the work here it is important that you provide your opinions and comments for full credit.
Attached
A. Excel Data Set 1: OxHome
B. Excel Data Set 2: UnitedOil
C. Excel Data Set 3: SalesPerf
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