1.2 Design, Description, Inference Name ______
STATS
1. The Harvard Medical School study mentioned in Scenario 2 used about 22,000 male physicians. The method of deciding whether a given person would receive aspirin or placebo was essentially made by flipping a coin. About 11,000 were assigned to take aspirin, and about 11,000 to take the placebo. The researchers described results by the percentage of each group that had a heart attack during the study. This was 0.9% for those taking aspirin and 1.7% for those taking placebo. They then used statistical methods to predict that if all male physicians could have participated in this study, the percentage having a heart attack would have been lower for those taking aspirin.a) Highlight the design in YELLOW
b) Highlight the description in PINK
c) Highlight the inference in BLUE
2. The Current Population Survey (CPS) is a monthly survey of households conducted by the U.S. Census Bureau of Labor Statistics. It provides a comprehensive body of data on the labor force, employment, and unemployment. A CPS of about 60,000 households indicated that of those households, 8.0% of the whites, 23.4% of the blacks, and 22.7% of the Hispanics had annual income below the poverty level. Using these data, a statistical method makes the prediction that the percentage of all black households in the United States that had income below the poverty level was at least 22% but no greater than 25%.
a) Highlight the design in YELLOW
b) Highlight the description in PINK
c) Highlight the inference in BLUE
3. One year the General Social Survey,given to 20,000 adult Americans, asked, “About how many good friends do you have?” Of the 819 people who responded, 6% reported having only 1 good friend.
a) Identify the sample
b) Identify the population
c) Identify the statistic reported.
4. The Florida Poll of about 1200 Floridians has been given annually since 1988 to track opinions on a wide variety of issues. In 2006 the poll asked, “How concerned are you about the problem of global warming?” The possible responses were (very concerned, somewhat concerned, nor very concerned, haven’t hear about it). The poll reported percentages (44, 30, 21, 5) in these categories.
a. Identify the sample and the population.
SAMPLE:
POPULATION:
b. Are the percentages quoted statistics or parameters? Why?
5. The medical study mentioned in Scenario 2 and in Exercise 1.1 conducted an experiment with 22,000 male physicians, to investigate whether regular intake of aspirin reduces the chance of heart attack compared to taking placebo. The study concluded that for all male physicians, aspirin would be more effective than placebo.
a. Identify the sample and the population.
SAMPLE:
POPULATION:
b) Identify the inference made.
6. The job placement center at your school surveys all graduating seniors at the school. Their report about the survey provides numerical summaries such as the average starting salary and the percentage of students earning more than $30,000 a year.
a. Are these statistical analyses descriptive or inferential? Explain.
b. Are these numerical summaries better characterized as statistics or as parameters?
7. A historian wants to estimate the average age at marriage for women in New England in the early nineteenth century. Within her state archives she finds marriage records for the years 1800-1820. She takes a sample of those records, noting the age of the bride for each. The average age in the sample is 24.1 years. Using a statistical method, she finds a margin of error and estimates that the average age of brides for the population was between 23.5 and 24.7.
a. What part of this example is descriptive, giving a summary of the data? Highlight in YELLOW
b. What part of this example is inferential, making a prediction about the population? Highlight in PINK
c. To what population does the inference refer?
d. Is the average age in the sample of 24.1 a statistic or a parameter? How did you decide?
8. Consider the population of all students at your school. A certain proportion support mandatory national service (MNS) following high school. Your friend randomly samples 20 students from the school, and uses the sample proportion who support MNS to predict the population proportion at the school. You take your own, separate random sample of 20 students, and find the sample proportion that supports MNS.
a. For the two studies, are the populations the same?
b. For the two studies, are the sample proportions necessarily the same? Explain.
9. We’ll see that the amount by which results vary from sample to sample depends on the sample size. In an election with two candidates, Smith and Jones, suppose Smith receives close to 50% of all votes. An exit poll is taken on the day of the election to predict the winner.
Which case would you find more surprising –
OPTION A: taking an exit poll of 10 voters and finding that 0% of them voted for Smith,
or OPTION B: taking an exit poll of 1000 voters and finding that 0% of them voted for Smith
Explain.