Chapter 12: Q.7 (page 797)
A 95% confidence interval for the slope B of the population regression line is
A 95% confidence interval for the slope B of the population regression line is41391983396742" width="9" height="19" role="math">
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Weeds among the corn Refer to Exercise 13.
(a) Construct and interpret a 90% confidence interval for the slope of the true regression line. Explain how your results are consistent with the significance test in Exercise 13.
(b) Interpret each of the following in context:
(i) 8
(ii)
(iii) The standard error of the slope
Beer and BAC How well does the number of beers a person drinks predict his or her blood alcohol content (BAC)? Sixteen volunteers with an initial BAC of drank a randomly assigned number of cans of beer. Thirty minutes later, a police officer measured their BAC. Least-squares regression was performed on the data. A residual plot and a histogram of the residuals are shown below. Check whether the conditions for performing inference about the regression model are met.
Boyle’s law If you have taken a chemistry class, then you are probably familiar with Boyle’s law: for gas in a confined space kept at a constant temperature, pressure times volume is a constant (in symbols, ). Students collected the following data on pressure and volume using a syringe and a pressure probe.
(a) Make a reasonably accurate scatterplot of the data by hand using volume as the explanatory variable.
Describe what you see.
(b) If the true relationship between the pressure and volume of the gas is , we can divide both sides of this equation by to obtain the theoretical model , or . Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).
(c) Use the graph below to identify the transformation that was used to linearize the curved pattern in part (a).
Is wine good for your heart? A researcher from the University of California, San Diego, collected data on average per capita wine consumption and heart disease death rate in a random sample of 19 countries for which data were available. The following table displays the data.
(a) Is there statistically significant evidence of a negative linear relationship between wine consumption and heart disease deaths in the population of countries? Carry out an appropriate significance test at the level.
(b) Calculate and interpret a 95% confidence interval for the slope of the population regression line.
Which of the following sampling plans for estimating the proportion of all adults in a medium-sized town who favor a tax increase to support the local school system does not suffer from undercoverage bias?
(a) A random sample of names from the local phone book
(b) A random sample of parents whose children attend one of the local schools
(c) A sample consisting of people from the city who take an online survey about the issue
(d) A random sample of homeowners in the town
(e) A random sample of people from an alphabetical list of all adults who live in the town
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