1. Explain, clearly and briefly, in your own words the following.
2. Explain, clearly and briefly, in your own words the following.
4. Some researchers have found that there is a positive correlation between coffee drinking and the risk of heart disease.
5. A marketing firm wanted to estimate the average amount spent by shoppers entering a small grocery store in midtown. For 130 randomly selected customers, the mean amount spent was $24.50 and the standard deviation was $4.80.
6. At the beginning of the fall semester, a poll showed that 44% of the students in dormitories at a large university wanted loud music turned off at 10 o'clock on nights before school days. Proponents of the music curfew conducted a second poll in November hoping to show that the percentage had increased as exams drew near. 120 students were randomly selected and they found that 63 of them favored the music curfew.
7. Considering how common international travel has become, you are asked to investigate the number of resident U.S. citizens in a country (x) and the number of U.S. tourists in the same country (y). You use the Statistical Abstract of the United States, 1994 and randomly choose 12 countries for your study. The information you collected is recorded below:
|Country||x = number of U.S. citizens who are residents (in thousands)||y = number of U.S. tourists (in thousands)|
8. A sociologist wishes to see whether the number of years of college a person has completed is related to his/her place of residence. A sample of 1000 people is selected and classified as given below. Test the hypothesis that the years of college and the residence location are independent. Test at the 5% level of significance.
|Location||No College||College Degree||Graduate Degree||Total|
9. For a group of 25 men subjected to a stress test, the mean number of heartbeats per minute was 126 and the standard deviation was 4. Assume the measure is approximately normal.
10. The table below shows data from the Statistical Abstract of the United States, 1994. It shows the relationship between gender and ethnic groups among Americans of Hispanic descent who participate in the work force. (A group of 14,770,000 workers.) A social scientist is interested in sampling these ethnic groups to see if gender and ethnic group are independent for Hispanic-American workers. His sample results are listed.
11. A researcher is interested in estimating the average salary of police officers in a city. She wants to be 95% sure that her estimate is correct to within $200 of the true mean salary. A pilot study was conducted to determine an estimate for standard deviation to be $1250. How large a sample will she need to measure the average salary to within $200?
13. If students are to evaluate a class and instructor properly, they need sufficient time to fill out the student evaluation form. One form under consideration has a claim that it takes only 10 minutes to fill out. To determine if the claim is correct, a random sample of 32 students were asked to fill in the form to evaluate their instructor for their first class on Monday. The times for completion in minutes were:
14. Consider the five income groups listed in the chart here.
|Group||% Distribution for the General Population|
|$15,000 - $34,999||33%|
|$35,000 - $49,999||17%|
|$50,000 - $74,000||16%|
The data is from the Statistical Abstract of the U.S., 1993. 1000 black families were surveyed and their income followed this pattern:
16. A study dealing with divorced couples gathered data on the length of time from marriage to separation. A random sample of 100 divorced couples had an average length of marriage of 5.9 years with a sample standard deviation of 2.0 years.
17. An automobile manufacturer is testing a new bumper that he feels will reduce the cost of repairs in front-end collisions at low speeds. Experience with the presently used bumper indicates that at 10 mph the cost of repair resulting from a front end collision has a mean of $325. To perform the test, the manufacturer equips 15 of his cars with the new bumper and has these 15 cars undergo front end collisions at 10 mph. Following this, the cars are repaired, and the cost of repair for each car is recorded. The sample mean x = $291.70 and the sample standard deviation s = $19.82.
18. A university science department has agreed upon Top 10% the grading policy shown here for an introductory course. The chairman of the department is not sure the policy was followed last semester. Since the introductory course has 2000 students in 50 sections, he does not want to tally all of these grades. Instead, he plans to take a random sample of 50 grades and perform a hypothesis test to see if the policy is followed.
The results of his sample are: A -- 10; B -- 10; C -- 10; D -- 14; F -- 6.
19. The following data gives the mean percent of items answered correctly on international mathematics tests in Algebra and Statistics for 8th grade students in the countries listed in 1981-1982. (Youth Indicators, 1988).
|Country||Algebra Score||Statistics Score|
20. In a study of 200 accidents that required treatment in an emergency room, 80 of the accidents occurred at home.
21. In 1985, 27% of Americans believed that "We should keep our doors open to immigration." In a survey of 1,108 adult Americans who participated in a Time Magazine/CNN survey in September, 1993, 24% then believed this statement.
22. It is claimed that a new treatment for prolonging the lives of cancer patients is more effective than the standard one. With the standard treatment the mean survival period was shown to be 4.3 years. The new treatment was administered to 20 patients and the duration of their survival (measured in years) is recorded here:
23. What role does the Central Limit Theorem play in inferential statistics?
24. The college president asks the statistics teachers to estimate the average age of the students at their college. How large a sample is necessary? The statistics teachers decide the estimate should be accurate to within 1 year and be at a 99% confidence level. From a previous study, the standard deviation of the ages was found to be 2.5 years.
25. The sociology department is conducting a study to see if the percentage of dual income families has increased over the past 15 years. Fifteen years ago, studies showed that in 45% of the families studied, both spouses worked outside the home. A study this year shows that for a random sample of 400 families in which both spouses were present, both spouses earn income in 210 of the cases.
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