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Chapter 3: Q4 (page 127)
Sleep Variance The standard deviation of the sample values in Exercise 1 is 1.3 hours. What is the variance (including units)?
The variance is 1.7
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Why Divide by n − 1? Let a population consist of the values 9 cigarettes, 10 cigarettes, and 20 cigarettes smoked in a day (based on data from the California Health Interview Survey). Assume that samples of two values are randomly selected with replacement from this population. (That is, a selected value is replaced before the second selection is made.)
a. Find the variance of the population {9 cigarettes, 10 cigarettes, 20 cigarettes}.
b. After listing the nine different possible samples of two values selected with replacement, find the sample variance (which includes division by n - 1) for each of them; then find the mean of the nine sample variances .
c. For each of the nine different possible samples of two values selected with replacement, find the variance by treating each sample as if it is a population (using the formula for population variance, which includes division by n); then find the mean of those nine population variances.
d. Which approach results in values that are better estimates of part (b) or part (c)? Why? When computing variances of samples, should you use division by n or n - 1?
e. The preceding parts show that is an unbiased estimator of . Is s an unbiased estimator of ? Explain
In Exercises 21–28, use the same list of Sprint airport data speeds (Mbps) given for Exercises 17–20. Find the indicated percentile or quartile.
P75
USA Today published a list consisting of the state tax on each gallon of gas. If we add the 50 state tax amounts and then divide by 50, we get 27.3 cents. Is the value of 27.3 cents the mean amount of state sales tax paid by all U.S. drivers? Why or why not?
Critical Thinking. For Exercises 5–20, watch out for these little buggers. Each of these exercises involves some feature that is somewhat tricky. Find the (a) mean, (b) median, (c) mode, (d) midrange, and then answer the given question
Firefighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while lighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of center?
20 18 23 30 20 12 24 9 25 15 8 11 15 34
In Exercises 5–20, find the range, variance, and standard deviation for the given sample data. Include appropriate units (such as “minutes”) in your results. (The same data were used in Section 3-1, where we found measures of center. Here we find measures of variation.) Then answer the given questions.
Fireighter Fatalities Listed below are the numbers of heroic firefighters who lost their lives in the United States each year while fighting forest fires. The numbers are listed in order by year, starting with the year 2000. What important feature of the data is not revealed by any of the measures of variation?
20 18 23 30 20 12 24 9 25 15 8 11 15 34
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