12 May HOW MUCH ADVANTAGE DOES THE YANKEE HOME FIELD PROVIDE?
In the 1996 regular baseball season, the World Series Champion New York Yankees played 80 games at home and 82 games away. They won 49 of their home games and 43 of the games played away. We can consider these games as samples from potentially large populations of games played at home and away. How much advantage does the Yankee home field provide?
a. Find the proportion of wins for the home games. Do the same for the away games.
b. Find the standard error needed to compute a confidence interval for the difference in the proportions.
c. Compute a 90% confidence interval for the difference between the probability that the Yankees win at home and the probability that they win when on the road. Are you convinced that the 1996 Yankees were more likely to win at home?
2.
The state agriculture department asked random samples of Indiana farmers in each county whether they favored a mandatory corn check off program to pay for corn product marketing and research. In Tippecanoe County, 263 farmers were in favor of the program and 252 were not. In neighboring Benton County, 260 were in favor and 377 were not.
a. Find the proportions of farmers in favor of the program in each of the two counties.
b. Compute a 95% confidence interval for the difference between the proportions of farmers favoring the program in Tippecanoe County and in Benton County. Do you think opinions differed in the two counties?
3.
A study of chromosome abnormalities and criminality examined data on 4124 Danish males born in Copenhagen. The study used the penal registers maintained in the offices of the local police chiefs and classified each man as having a criminal record or not. Each was also classified as having the normal male XY chromosome pair or one of the abnormalities XYY or XXY. Of the 4096 men with normal chromosomes, 381 had criminal records, while 8 of the 28 men with chromosome abnormalities had criminal records. Some experts believe that chromosome abnormalities are associated with increased criminality. Do these data lend support to this belief? Report your analysis and draw a conclusion.
A recent study examined the association between high blood pressure and increased risk of death from cardiovascular disease. There were 2676 men with low blood pressure and 3338 men with high blood pressure. In the low-blood-pressure group, 21 men died from cardiovascular disease; in the high-blood-pressure group, 55 died.
a. Compute the 95% confidence interval for the difference in proportions.
b. Do the study data confirm that death rates are higher among men with high blood pressure? State hypotheses, carry out a significance test, and give your conclusions.
4.
Find the p-value for each by filling in the table (don’t forget to complete the calculator command):
Degrees of Freedom x2 Calculator Command p-value
4 5 x2cdf(
4 10 x2cdf(
4 15 x2cdf(
4 20 x2cdf(
3 15 x2cdf(
4 15 x2cdf(
5 15 x2cdf(
6 15 x2cdf(
5.
Sarah is running a chi-squared Goodness of Fit test to test whether the claimed proportions of candy colors in assorted bags of candy are different than claimed by the company. She takes a random sample of 300 pieces of candy from assorted bags. The company claims the following proportions of colors in assorted bags:
Green Yellow Red Blue
0.2 0.3 0.3 0.2
What are the expected results of each color?
6.
A regular 6-sided die is tossed 200 times with the faces turning up as follows:
Number 1 2 3 4 5 6
Frequency 34 28 35 31 31 41
Is there reason to suspect that the die is not fair? Run a complete test.
7.
What does the chi-squared test of independence really test?
8.
When working with a two-way table, describe how you find the expected counts for each cell in the table.
9.
A survey was conducted of 200 people and their responses were categorized by party affiliation and opinion on gun control. The results are shown in this table:
Observed Favor Oppose Unsure Total
Democrat 44 48 18 110
Republican 32 48 10 90
Total 76 96 28 200
a. Fill in the table below with the expected counts.
Expected Favor Oppose Unsure Total
Democrat 110
Republican 90
Total 76 96 28 200
b. Based on this sample, does a person’s opinion on gun control depend on party affiliation, at the .05 level of significance?
10.
There are four major blood types in humans: O, A, B, and AB. In a study conducted using blood specimens from the Blood Bank of Hawaii, individuals were classified according to blood type and ethnic group. The ethnic groups were Hawaiian, Hawaiian-white, Hawaiian-Chinese, and white. Assume that the blood bank specimens are random samples from the Hawaiian populations of these ethnic groups.
Ethnic Group —
Blood Type Hawaiian Hawaiian White Hawaiian Chinese White
O 1,903 4,469 2,206 53,759 /div>
A 2,490 4,671 2,368 50,008
B 178 606 568 16,252
AB 99 236 243 5,001
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