he density netion of the cont variable X, the total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a pe- riod of one year, is given in Exercise 3.7 on page 92 ious random as 0 < x < 1, x, f(x) = {2- x, 1< x < 2, (0, elsewhere. Find the average number of hours per year that families run their vacuum cleaners.

A traffic safety company publishes reports about motorcycle fatalities and helmet use. In the first accompanying data table, the distribution shows the proportion of fatalities by location of injury for motorcycle accidents. The second data table shows the location of injury and fatalities for 2061 riders not wearing a helmet. Complete parts (a) and (b) below. Click the icon to view the tables. (a) Does the distribution of fatal injuries for riders not wearing a helmet follow the distribution for all riders? Use α = 0.05 level of significance. What are the null and alternative hypotheses? O A. Ho: The distribution of fatal injuries for riders not wearing a helmet follows the same distribution for all other riders. H₁: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders. B. Ho: The distribution of fatal injuries for riders not wearing a helmet does not follow the same distribution for all other riders. H₁: The…

Summarize the definitions for linear correlation, quadratic correlations and exponential correlations. Provide an example graph of each of the types of correlation along with your summarized definitions.

A nutritionist collects data from 25 popular breakfast cereals. For each cereal, the number of calories per serving is plotted on the x-axis against the number of milligrams of sodium on the y-axis. The value of r for the resulting scatterplot is 0.83. How would the value of the correlation coefficient, r, change if sodium was plotted on the x-axis and calories plotted on the y-axis? The value of r would increase. The value of r would not change. The value of r would change to –0.83. The value of r could increase or decrease, depending of the strength of the new relationship.

Suppose data are collected concerning the weight of a person in pounds and the number of calories burned in 30 minutes of walking on a treadmill at 3.5 miles per hour. How would the value of the correlation coefficient, r, change if all of the weights were converted to kilograms?

The trend of thinner beauty pageant winners has generated charges that the contest encourages unhealthy diet habits among young women. Listed below are body mass indexes (BMI) for beauty pageant winners from two different time periods. Find the coefficient of variation for each of the two sets of data, then compare the variation. BMI (from the 1920s and 1930s): 20.5 21.9 22.1 22.3 20.3 18.7 18.8 19.4 18.3 19.2 BMI (from recent winners): 19.4 20.3 19.6 20.3 17.7 17.9 19.2 18.7 17.7 16.8 The coefficient of variation for the BMI's of beauty pageant winners from the 1920s and 1930s is %. (Round to one decimal place as needed.) The coefficient of variation for the BMI's of recent beauty pageant winners is %. (Round to one decimal place as needed.) Is there a difference in variation between the two data sets? O A. The BMI's of beauty pageant winners from the 1920s and 1930s have considerably less variation than the BMI's of recent winners. O B. The BMI's of recent beauty pageant winners have…

Calculate test statistic Decide whether to reject or fail to reject

There is a negative correlation between the average litres of wine consumed by residents of a country and the incidence of national coronary deaths. Explain why correlation in this case does not imply causation by suggesting a third variable z that explains the correlation. Is z a common response or a confounding variable? Draw a digraph illustrating the between x, y, and z