Section 7: Introduction to Statistics

1) Identify which sampling distributions have high or low bias, high or low variability. How does the mean of the statistic compare in each case to the parameter? Is the standard deviation a comparatively large or small number?

2.) Identify whether each boldface number is a parameter or a statistic.

a) The Bureau of Labor Statistics announces that last month it interviewed all members of the labor force in a sample of 60,000 households. 6.2% of those interviewed were unemployed.

b) A telemarketing firm in Los Angeles uses a device that dials residential telephone numbers at random. Of the first 100 numbers dialed, 43 are unlisted. This is not surprising, because 52% of all Los Angeles residential phones are unlisted.

c) we're told that the probability that a suspicious coin will land heads is 0.4 It's tossed 300 times, and 129 times it lands heads.

3) We wish to know what percentage of people find it annoying when people walk up to them on the street and ask them stupid questions. Sam walks up to 300 people, and 210 of them find it annoying. George walks up to 2000 people, and 1400 find it annoying. Each concludes that 70% of people find such things annoying. Which, or neither, is more justified in his conclusion?

4) Sam and George try the same approach with telephone calls. Sam calls up 500 randomly chosen people in their city, and 450 find it annoying. George calls up 500 randomly chosen people in their state, and 450 find it annoying. Sam concludes that 90% of people in their city find such calls annoying; George concludes that 90% of the people in their state find it annoying. Which, or neither, is more justified in his conclusion?

5) Sam and George try the telephone thing again. Sam calls up 1% of the people in a small town, and George calls up 1% of the people in a much larger city. Which, or neither, will be more justified in his conclusion as to the percent of people in these areas who find such calls annoying?

Answers:

1) (a) high bias, high variability, mean of statistic is far from parameter, standard deviation of statistic is large (b) low bias, low variability, mean is close to parameter, small st. dev. (c) low bias, high variability, mean is close to parameter, large st. dev. (d) high bias, low variability, mean is far from parameter, small st. dev.

2) (a) statistic (b) statistic, parameter (c) parameter, statistic

3) George's larger sample means that the standard deviation of his statistic is smaller. Repeated samples will vary less in their results. He can be more confident.

4) Sam and George have equal sample sizes under similar conditions. The standard deviations of their statistics will be about the same, since it's determined mostly be sample size. The number of people not in the sample is irrelevant. Repeated samples will vary about the same. They can be about equally confident about the results.

5) 1% of a larger number is larger, so George's sample size is much larger than Sam's. The standard deviation of his statistic will be much smaller; i.e., in repeated samples he'll get results that vary less widely. He can be more confident.