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# Comparing the effectiveness of programs in test Hypothesis

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The federal government recently granted funds for a special program designed to reduce crime in high-crime areas. A study of the results of the program in 8 high-crime areas of Miami, Florida, yielded the following results: Number of crimes by are
A B C D E F G H
Before 14 7 4 5 17 12 8 9
After 2 7 3 6 8 13 3 5

Has there been a decrease in the number of crimes since the inauguration of the program? Use the .01 significance level. Estimate the P-value

1a. List null hypothesis and alternative hypothesis in your significance testing, if we want to know whether the crime is significantly reduced.
1b. If conducting this significance testing at the significance level of 0.05, what is the critical value for this testing you should use?
1c. Calculate the test statistic. (Note: keep two decimal places for your result.)
1d. Compare the test statistic in 1c to the critical value in 1b and then reach a statistical conclusion.
1e. Translate the conclusion in 1d into some business language (actually, not exactly "business"). Note: as mentioned in class, when you are interpreting conclusion, do not focus on those mathematical values, e.g. number of crime. Instead, ask yourself what they are essentially interested in, according to nature of the problem.
1f. What is p-value for this question?

2. Marketing department in one company needs to decide which one of the two newspaper advertisements, A and B, recently produced for their product will be more effective. Then, they will publish the more effective advertisement. To help the decision, they randomly select two groups of people from target market segment of this product. They let one group of people read Advertisement A and give their ratings on the Ads scaled from 1-worst to 5-best. In the meantime, they let the other group do the same thing for Advertisement B. Next, they conduct a hypothesis testing comparing average ratings of the two groups. Now, does the way in which the department conducts the study look problematic to you? Why or why not?

The Roper Organization conducted identical surveys 5 years apart. One question asked of women was Are most men basically kind, gentle, and thoughtful? The earlier survey revealed that, of the 3,000 women surveyed, 2,010 said that they were. The later revealed 1,530 of the 3,000 women surveyed thought that men were kind, gentle, and thoughtful. At the .05 level, can we conclude that women think men are less kind, gentle, and thoughtful in the later survey compared with the earlier one?...

2a. List null hypothesis and alternative hypothesis in your significance testing if we want to know if significantly smaller proportion of women considers mean kind gentle and thoughtful five years later.
2b. If conducting this significance testing at the significance level of 0.05, what is the critical value for this testing you should use?
2c. Calculate the test statistic. (Note: keep two decimal places for your result.)
2d. Compare the test statistic in 2c to the critical value in 2b and then reach a statistical conclusion.
2e. Translate the conclusion in 2d into business language (well, again, it is not exactly "business" knowledge)
2f. What is p-value for this question?

A number of minor automobile accidents occur at various high-risk intersections...
A number of minor automobile accidents occur at various high-risk intersections in Teton County despite traffic lights. The Traffic Department claims that a modification in the type of light will reduce these accidents. The county commissioners have agreed to a proposed experiment. Eight intersections were chosen at random, and the lights at those intersections were modified. The numbers of minor accidents during a six-month period before and after the modifications were:

Number of Accidents
A B C D E F G H
Before modification 5 7 6 4 8 9 8 10
After modification 3 7 7 0 4 6 8 2

At the .01 significance level is it reasonable to conclude that the modification reduced the number of traffic accidents?

3a. List null hypothesis and alternative hypothesis in your significance testing, if we want to know whether number of accidents is significantly reduced.
3b. If conducting this significance testing at the significance level of 0.01, what is the critical value for this testing you should use?
3c. Calculate the test statistic. (Note: keep two decimal places for your result.)
3d. Compare the test statistic in 3c to the critical value in 3b and then reach a statistical conclusion.
3e. Translate the conclusion in 3d into business language (well, again, again, it is not exactly "business" knowledge)
3f. What is p-value for this question?

There are two major Internet providers in the Colorado Springs, Colorado, area, one called
HTC and the other Mountain Communications. We want to investigate whether there is a
difference in the proportion of times a customer is able to access the Internet. During a oneweek
period, 500 calls were placed at random times throughout the day and night to HTC.
A connection was made to the Internet on 450 occasions. A similar one-week study with
Mountain Communications showed the Internet to be available on 352 of 400 trials. At the
.01 significance level, is there a difference in the percent of time that access to the Internet
is successful?

4a. List null hypothesis and alternative hypothesis in your significance testing, if we want to know whether HTC has significantly higher successful connection rate.
4b. If conducting this significance testing at the significance level of 0.05, what is the critical value for this testing you should use?
4c. Calculate the test statistic. (Note: keep two decimal places for your result.)
4d. Compare the test statistic in 4c to the critical value in 4b and then reach a statistical conclusion.
4e. Translate the conclusion in 4d into business language.
4f. What is p-value for this question?

A consumer organization wants to know if there is a difference in the price of a particular
toy at three different types of stores. The price of the toy was checked in a sample of five discount toy stores, five variety stores, and five department stores. The results are shown below. (Use the .05 signifcance level to conduct the test).

Discount Toy Variety Department

\$12 15 19
13 17 17
14 14 16
12 18 20
15 17 19

5a. Do the test in Excel. Copy and paste the Excel ANOVA output here.
5b. According the ANOVA output in 5a, do you reject or fail to reject the ANOVA null hypothesis at the 0.05 significance level? More important, justify your answer based on either critical value or p-value.