Suppose that the relationship between a response variable y and an explanatory variable x is modelled by . Which of the following scatterplots would approximately follow a straight line?
(a) A plot of y against x
(b) A plot of y against log x
(c) A plot of log y against x
(d) A plot of log y against log x
(e) None of (a) through (d)
The scatterplots that approximately follow a straight line is option (c) A plot of log y against x.
The relationship between a response variable y and an explanatory variable x is modelled by .
The given equation is
The scatterplot will not be a straight line since this equation represents an exponential function, which is not linear.
If we multiply both sides of the equation by the logarithm, we get:
This is a linear equation with variables log and and thus the scatterplot will be a straight line in this case.
Do hummingbirds prefer store-bought food made from concentrate or a simple mixture of sugar and water? To find out, a researcher obtains identical hummingbird feeders and fills , chosen at random, with store-bought food from concentrate and the other with a mixture of sugar and water. The feeders are then randomly assigned to possible hanging locations in the researcher’s yard. Which inference procedure should you use to test whether hummingbirds show a preference for store-bought food based on amount consumed?
(a) A one-sample z test for a proportion .
(b) A two-sample z test for a proportion .
(c) A chi-square test for association/independence .
(d) A two-sample t test .
(e) A paired t test .
Foresters are interested in predicting the amount of usable lumber they can harvest from various tree species. They collect data on the diameter at breast height (DBH) in inches and the yield in board feet of a random sample of Ponderosa pine trees that have been harvested. (Note that a board foot is defined as a piece of lumber inches by inches by inch.) A scatterplot of the data is shown below
(a) Some computer output and a residual plot from a least squares regression on these data appear below. Explain why a linear model may not be appropriate in this case.
(B) Use both models to predict the amount of usable lumber from a Ponderosa pine with diameter inches. Show your work.
(c) Which of the predictions in part (b) seems more reliable? Give appropriate evidence to support your choice.
Suppose that the mean weight of a certain type of pig is with a standard deviation of. The weight distribution of pigs tends to be somewhat skewed to the right. A random sample of pigs is taken. Which of the following statements about
the sampling distribution of the sample mean weight is true?
(a) It will be Normally distributed with a mean of and a standard deviation of
(b) It will be Normally distributed with a mean of and a standard deviation of
(c) It will be approximately Normally distributed with a mean of and a standard deviation of
(d) It will be approximately Normally distributed with a mean of and a standard deviation of
(e) There is not enough information to determine the mean and standard deviation of the sampling distribution.
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