Chapter 9 Hypothesis Testing
Textbook Problems: 26,30 (Show all your work and discuss your responses)
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. 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.
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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: 28 (Show your work and discuss your responses)The video game satisfaction rating case28. Consider the sample of 65 customer satisfaction ratings given in table 12.11. Carry out chi-square goodness-of-fit test of normality for the population of all customer satisfaction ratings. Recall that we previously calculated x¯ =42.95 and s=2.6424 for the 65 ratings.
Table 12.11 |
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A Sample of 65 Customer Satisfaction ratings |
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39 |
46 |
42 |
40 |
45 |
44 |
44 |
44 |
45 |
45 |
44 |
46 |
46 |
46 |
41 |
46 |
46 |
38 |
40 |
40 |
41 |
43 |
38 |
48 |
39 |
42 |
39 |
47 |
43 |
47 |
43 |
44 |
41 |
42 |
40 |
44 |
39 |
43 |
36 |
41 |
44 |
41 |
42 |
43 |
43 |
41 |
44 |
45 |
42 |
38 |
45 |
45 |
46 |
40 |
44 |
44 |
47 |
42 |
44 |
45 |
45 |
43 |
45 |
44 |
43 |
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. 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: All excel data sets
Textbook Chapter 13 Problems: 16,26 & the following two other problems:Question 13.16 and p. 482 outputs up loaded as a file.
Question 13.26 Uploaded as a file
*Excel Data Sheets UploadedOther 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. 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.
*483-484 questions Uploaded
A. Excel Data Set 1: SalesAdv
B. Excel Data Set 2: StockRtn
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Textbook Chapter 14 Problems: 18, 24 & the following two other problems:*Questions 14.18 and 14.24 uploaded
Other Problems:Run the regression model for the following two 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.
A. Excel Data Set 2: UnitedOil
B. Excel Data Set 3: SalesPerf
*7 steps: Uploaded p. 540
*If you need the examples from my textbook I can upload them. Only need to due 2 out of the 3.
Essays: Complete ANY TWO the following essays providing your own opinions and examples. The length of each essay should be at least one page in length.
- Hypothesis testing is one of the most important and widely used topics in statistics.It is a statistical procedure that is used to provide evidence in favor of some statement or claim hence the word hypothesis. Hypothesis testing Example (see page 328, The Trash Bag Case as an example as a quick review) A company is claiming that its 30-gallon trash bags can hold 50 pounds of trash before they break. The hypothesis test also leads to making the right claim or making a type I or Type II error. (see page 332)
Type I rejecting a correct claim (failing to claim true results)
Type II not rejecting a correct claim. (misleading claim/advertisement)
Question: Please provide a real world example of how you would use the hypothesis test, also listing one benefit and concern that you may have.
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B. The Chi-Square & Goodness of Fit test evaluates whether data falling into several categories do so with a hypothesized set of probabilities.
We want to compare observed frequencies with those of expected frequencies to determine the outcome and if variables differ from one another. We also want to determine if the null hypothesis is true or do we reject it.
For example, taking the Microwave oven case on page 442, Example 12.1 in the textbook that compares consumer preferences in Milwaukee with those of Cleveland if Milwaukee preferences are different the store will then consider changing its policies for which ovens to stock.
Question:Provide and discuss a real example of a Chi-Square distribution also discussing one pro and one con.===============================================================
C. Regression analysis is a good way for management to make business decisions. This is the study of relationships between one or more variables. One compares dependent variables (y) and independent variables (x) to attempt to describe and predict the best possible outcomes. Multiple regression uses more than one independent variable (x) which is a better predicator for examples like what effects the sale price of a house, is not only affected by historical prices but also by comparing crime statics, comparable selling prices, school district and others factors. This makes multiple regression a little more useful than simple regression.
If you look at the Tasty Sub examples 13.1 on page 465 and example 14.1 on 525 thesegive a good idea of the use of both simple and multiple regression. In chapter 13 yearly revenues are affected (dependent) on population size as indicated on page 466 and in chapter 14 they not only use population size but also business ratings to provide a better relationship on revenues.
Question: Provide and discuss an example of regression and how it can be used in the business world.
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