Math 251, Practice Questions on Topics Since 3rd Test
(Linear Regression, Goodness of Fit, Analysis of Variance)
1. (From p. 594 #12) Let x be the age of a licensed driver in years. Let y be the percentage of all fatal accidents (for a given age) due to failure to yield the right of way. For example, the first data pair says that 5% of all fatal accidents of 37-year olds are due to failure to yield the right of way. The Wall Street Journal reported the following data:
x 37 47 57 67 77 87
y 5 810163043
Note: x = 372 y = 112 x2 = 24,814 y2 = 3194 xy =8254
(a) Draw a scatter plot of the data and find the equation of the least squares line.
(b) Use your line from (a) to predict the percentage of fatal accidents due to failure to yield right of way for 40-year olds.
(c) Use the regression line in (a) to predict the age for which the percentage of fatal accidents due to failure to yield is 20%.
(d) Do the data appear to be positively or negatively correlated? Explain.
(e) Compute the correlation coefficient, does its sign agree with your answer in (d)? Does it suggest that there is a good linear fit?
(f) Compute the coefficient of determination, and interpret what it means.
2. (From p. 655#3) The type of raw material used to construct stone tools found at the archaeological site Casa del Rito is shown below. A random sample of 1486 stone tools was obtained from a current excavation site.Raw Material / Regional Percent of
Stone Tools / Observed Number of Tools
Tools at Current Site
Basalt / 61.3% / 906
Obsidian / 10.6% / 162
Welded tuff / 11.4% / 168
Pedernal chert / 13.1% / 197
Other / 3.6% / 53
(a) Use a 1% level of significance to test the claim that the regional distribution of raw materials fits the current excavation site. Make sure to state null and alternative hypotheses, the critical region and the conclusion.
(b) Repeat (a) using a 5% level of significance.
3. (From p. 694 #9) A sociologist studying New York City ethnic groups wishes to determine if there is a difference in income for immigrants from four different countries during there first year in the city. She obtained the data in the following table from a random sample of immigrants from these countries (incomes in thousands of dollars). Use a 0.05 level of significance to test the claim that there is no difference in the earnings of immigrants from the four different countries.Country I / Country II / Country III / Country IV
12.7 / 8.3 / 20.3 / 17.2
9.2 / 17.2 / 16.6 / 8.8
10.9 / 19.1 / 22.7 / 14.7
8.9 / 10.3 / 25.2 / 21.3
16.4 / 19.9 / 19.8
(a) State the null and alternative hypotheses.
(b) What assumptions should be made on the populations in order to conduct the test?
(c) State the critical region for the test.
(d) Given that MSBET = 79.408 and MSW = 17.223 for this data, report the conclusion of the hypothesis test.
(e) Repeat the test at the 1% level of significance.