1) You are a struggling college student and look for the best deals you can find on things you need (including your nightly cup of coffee before class). Pete's coffees opens a store near the Starbucks that you have been going to and advertises a promotion that will get you a free cup of coffee. When you go to Pete's, they will give you a reward card to scratch off. The sign claims that more than 50% of the cards result in a free cup of coffee or a free cappuccino. You've been going to Pete's and haven't gotten a card with a free cup yet so you want to test their claim. You sample 25 other students who have been to Pete's and find that 52% of them say they have received a free cup of coffee or cappuccino. Test the store's claim at the .10 significance level. Be sure to show your claim and hypothesis. What do you conclude about your null? What do you conclude about the claim?
2) In 2008 Pell and Smith State grants totaled about $4,000 per student. Although the federal government has cut the amount of Pell grants for 2012, Smith State publicizes that due to fundraising efforts they can offer students more than the 2008 amounts. You talk with your fellow students and find this claim hard to believe. Since you are taking statistics, you decide to take a sample to test the university claim. You take a sample of 31 students and find a mean award of $4,162 with a standard deviation of $754. Test the university's claim at the .10 significance level. Be sure to show the claim and your null and alternative hypothesis. What did you conclude about your null hypothesis? What do you conclude about the claim?
3) What is Type I error? How do we correct for it using the significance level? What happens when we do?
4) What is Type II error? How do we correct for it using the significance level? What happens when we do?
5) How can we correct for Type I and Type II error at the same time?
6)There is some evidence that individuals who start exercising without properly warming are more prone to injury. You do a survey to determine if stretching before exercising is related to the number of injuries that an individual might have. The results are shown in the contingency table below. Use the Chi-Square of association (relationship) to test the hypothesis that stretching before exercising is not related to the occurrence of an injury when exercising. Use the significance level of .01 to test the relationship. What do you conclude based on your data?
| |
Warm up stretching
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Total
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|
Result
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Yes
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No
|
|
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Injury
|
28
|
42
|
|
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No injury
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195
|
145
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|
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Total
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|
|
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7) Individuals use a wide variety of methods to prepare their taxes. Previous studies show that in 2002 the percentage for each method was as shown in the list below. You believe that there has been a change in how people do their taxes in the past 10 years, as home computers have been more prevalent. You have developed a new software for taxes and need to demonstrate to a financial backer that people have changed their habits. You do a random survey to determine how individuals prepared their taxes this year. Your data is contained in the table below. Using the previous percentages as a model, test your theory that there has been a change. Test at the .05 significance level. (HINT: use the percentages to determine the expected for each category based on the total in your sample. Be sure to convert the percentage to a decimal before you begin.)
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Method
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Previous %
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Survey data
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Expected
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(O-E)
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(O-E)2
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(O-E)2/E
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|
Accountant
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25%
|
91
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|
|
|
|
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By hand
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20%
|
60
|
|
|
|
|
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Computer Program
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35%
|
135
|
|
|
|
|
|
Friend/Family
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5%
|
25
|
|
|
|
|
|
Taxi prep service
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15%
|
50
|
|
|
|
|
| |
|
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