1. An advertising executive wants to determine if there is a relationship between a person's political bent and their level of education. He takes a random sample of people and sorts them according to the highest level of education completed. Based on the results in the table below, test at a 0.025 level of significance if a person's political preference is independent of their educational level.

Graduate School College High School

Liberal 170 160 75

Conservative 90 110 95

2. According to the Bureau of the Census, 12% of all naturalized U.S. citizens were born in Europe, 30% in Asia, 9% in the Caribbean, 38% in Central or South America, and the remaining 11% were born in other regions of the world. A random sample of 300 naturalized citizens in a major U.S. city showed that 35 people were born in Europe, 95 in Asia, 30 in the Caribbean, and 115 in Central or South America; and another 25 were born in other regions of the world.

At the 0.05 significance level, perform a goodness-of-fit-test to determine if the sample of people in this major city is random, i.e. representative of all naturalized citizens in the U.S.

3. According to Nabisco's specifications, the standard deviation in the diameter of chocolate chip cookies must be 0.25 inches. A random sample of 31 cookies shows a sample standard deviation of 0.30 inches. At the 0.10 significance level, determine if the cookies are being produced correctly.

4. A public opinion poll surveyed a simple random sample of 1000 voters. Respondents were classified by gender (male or female) and by voting preference (Republican, Democrat, or Independent). Based on the results in the table below, test at a 0.025 level of significance if a person's voting preference is dependent on his/her gender.

Republican Democrat Independent

Male 200 150 50

Female 250 300 50

5. Of all students of Asian background at Princeton High School (PHS), 35% are of Chinese, 20% are of Indian, 15% are of South Korean, and 10% are of Japanese descent; the remaining 20% are descended from other Asian nations. A sample of 200 student participants at the recent PHS Asian Festival included 56 students of Chinese, 50 of Indian, 24 of South Korean, and 16 of Japanese descent; another 54 were descendants of other Asian nations.

At the 0.05 significance level, perform a goodness-of-fit-test to determine if the sample of student participants at the festival is representative of all students of Asian background at PHS.

6. The regular machines used in a cereal packing plant inserts an average of 15.0 ounces of cereal in a box, with a standard deviation of 0.71 ounces. The plant will switch to a newer model of the machine if it reduces the standard deviation further, thereby packing a more consistent product. A test of 25 machines filled by the newer machine indicates a standard deviation of 0.67 ounces.

Should the plant replace the regular machines with the new? Test at the 0.10 significance level.