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Chapter 1: Q 100. (page 76)
Well rested? A random sample of 6 students in a first-period statistics class was asked how much sleep (to the nearest hour) they got last night. Their responses were 6, 7, 7, 8, 10, and 10. Calculate the standard deviation. Interpret this value.
The standard deviation is 1.6733 hours.
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Hit movies According to the Internet Movie Database, Avatar is tops based on box-office receipts worldwide as of January 2017. The following table displays data on several popular movies. Identify the individuals and variables in this data set. Classify each variable as categorical or quantitative.
Birthrates in Africa One of the important factors in determining population growth rates is the birthrate per 1000 individuals in a population. The dotplot shows the birthrates per 1000 individuals (rounded to the nearest whole number) for 54 African nations.
(a) Find the median.
(b) Without doing any calculations, explain how the mean and median compare.
Simpson鈥檚 paradoxAccident victims are sometimes taken by helicopter from the accident scene to a hospital. Helicopters save time. Do they also save lives? The two-way table summarizes data from a sample of patients who were transported to the hospital by helicopter or by ambulance.
(a) What percent of patients died with each method of transport? Here are the same data broken down by severity of accident:
(b) Calculate the percent of patients who died with each method of transport for the serious accidents. Then calculate the percent of patients who died with each method of transport for the less serious accidents. What do you notice?
(c) See if you can explain how the result in part (a) is possible given the result in part (b).
Note: This is an example of Simpson鈥檚 paradox, which states that an association between two variables that holds for each value of a third variable can be changed or even reversed when the data for all values of the third variable are combined.
Who buys cars? A car dealer keeps records on car buyers for future marketing purposes. The table gives information on the last 4 buyers.
Part (a). Identify the individuals in this data set.
Part (b). What variables were measured? Classify each as categorical or quantitative.
Value of a diploma Do students who graduate from high school earn more money than students who do not? To find out, we took a random sample of 371 U.S. residents aged 18 and older. The educational level and total personal income of each person were recorded. The data for the 57 non-graduates (No) and the 314 graduates (Yes) are displayed in the relative frequency histograms.
Part (a). Would it be appropriate to use frequency histograms instead of relative frequency histograms in this setting? Explain why or why not.
Part (b). Compare the distributions of total personal income for the two groups.
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