The following pages contain some summary statistics and graphics about the dataset.

Transcription

1 Thirty magazines were divided by educational level of their readers into three groups. Three magazines were randomly selected from each of the three groups. Six advertisements were randomly selected from each of the nine selected magazines. For each advertisement, the following variables were collected. Variable WDS SEN 3SYL MAG GRP Description number of words in advertisement copy number of sentences in advertising copy number of 3+ syllable words in advertising copy magazine (1 through 9 as shown below) Group 1: Highest educational level: 1. Scientific American 2. Fortune 3. The New Yorker Group 2: Medium educational level 4. Sports Illustrated 5. Newsweek 6. People Group 3: Lowest educational level 7. National Enquirer 8. Grit 9. True Confessions educational level of magazine (as above) The following pages contain some summary statistics and graphics about the dataset. 1

2 1) Very briefly describe the distributions of the three variables WDS, SEN, and 3SYL. Be sure to say something about center, shape, and spread. 2) Write a 95% confidence interval estimate for the mean number of words per advertisement in both group 1 and group 3. 3) Briefly compare the mean number of words in an advertisement from group 1 with the mean number of words in an advertisement from group 3 using your confidence intervals only. 2

3 4) Compare the mean number of 3 syllable words (3SYL) in advertisements for groups 1 and 3 - is there a significant difference? Are they equal? Indicate the test that you are using and clearly state your conclusion. Use α= ) Suppose a particular outcome from a random event has a probability of Which of the following statements represent correct interpretations of this probability? A) The outcome will never happen. B) The outcome will certainly happen two times out of every 100 trials. C) The outcome is expected to happen about two times out of every 100 trials. D) The outcome could happen, or it couldn't, the chances of either result are the same. 3

4 6) The Springfield Meteorological Center wanted to determine the accuracy of their weather forecasts. They searched their records for those days when the forecaster had reported a 70% chance of rain. They compared these forecasts to records of whether or not it actually rained on those particular days. The forecast of 70% chance of rain can be considered very accurate if it rained on: a. 95% to 100% of those days. b. 85% to 94% of those days. c. 75% to 84% of those days. d. 65% to 74% of those days. e. 55% to 64% of those days. 7) The distributions of SAT and LSAT scores are both approximately normal and symmetric. Veronica took both tests (at different times) and would like to know on which test her performance was better. Use the data given on each test to decide which score was better, relative to other people who took each test. 4

5 8) Create five quiz scores that provide a mean of 10 and a standard deviation of 0. 9) The salaries of the CEOs and the stock prices of 24 companies are shown in this scatterplot. A CEO uses this relation to argue there is a positive correlation between CEO salary and the Stock Price, and therefore, for the good sake of the company's stock value, his salary should be increased. Do you agree with his argument? Explain why or why not. Decide which probability distribution -binomial, geometric, or Poisson- applies to the question. You do not need to answer the probability question. 10) Given: The probability that a federal income tax return is filled out incorrectly with an error in favor of the taxpayer is 20%. Question: What is the probability that when the ten tax returns are randomly selected for an audit, the sixth return will contain only errors favoring the taxpayer? A) binomial B) Poisson C) geometric 5

6 11) A card company claims that 80% of all American college students send a card to their mother on Mother's Day. Suppose you plan to gather your own data to test this claim. You select a simple random sample of 400 American college students to determine the proportion of them who send a card to their mother on Mother's Day. Your sample indicates that 70% of the students sampled send a card to their mother on Mother's Day. Does this make you accept or reject the card companies claim? Justify your answer, carefully detailing your test and clearly stating your conclusion. Use α= ) In a one-way ANOVA with 3 groups, a rejection of the null hypothesis implies that a. the 3 population means are equal to each other b. the 3 sample means are equal to each other c. each population mean differs significantly from all other population means d. each sample mean differs significantly from all other sample means e. some subset of population means differs from some other subset of population means f. some subset of sample means differs from some other subset of sample means 6

7 13) According to Harper's magazine, the time spent by kids in front of the television set per year can be modeled by a normal distribution with a mean equal to 1500 hours and a standard deviation equal to 250 hours. A researcher followed a random sample of 49 children for one year and calculated the mean number of hours that these 49 children watched television. Approximate the probability that the sample mean is LESS than 1450 hours. Be sure to draw a picture for this problem, clearly labeling the graph with the z-value and shading the area that corresponds to the probability. 14) Twenty-six percent of people in the United States with Internet access go online to get news. A random sample of five Americans with Internet access is selected and asked if they get the news online. Clearly identify the values of n, p, and q, and list the possible values of the random variable x. Then find the probability that at least 3 of those sampled get the news online. 7