A popular, nationwide standardized test taken by high-school juniors and seniors may or may not measure academic potential, but we can nonetheless attempt to predict performance in college from performance on this test. We have chosen a random sample of fifteen students just finishing their first year of college, and for each student we've recorded her score on this standardized test (from 400 to 600) and her grade point average (from 0 to 4) for her first year in college. The data are shown below, with x denoting the score on the standardized test and y denoting the first-year college grade point average. The least-squares regression line for these data is
= XXXXXXXXXX0015x. This line is shown in the scatter plot in Figure 1.
Fill in the blank: For these data, standardized test scores that are less than the mean of the standardized test scores tend to be paired with grade point averages that _______ the mean of the grade point averages. (Greater or Lesser)
According to the regression equation, for an increase of one point in standardized test score, there is a co
esponding increase of how may points in grade point average?
From the regression equation, what is the predicted grade point average when the standardized test score is 1300? (Round your answer to at least two decimal place)
What was the observed grade point average when the standardized test score was 1300?
2. For a new study conducted by a fitness magazine, 280 females were randomly selected. For each, the mean daily calorie consumption was calculated for a September-Fe
uary period. A second sample of 220 females was chosen independently of the first. For each of them, the mean daily calorie consumption was calculated for a March-August period. During the September-Fe
uary period, participants consumed a mean of XXXXXXXXXXcalories daily with a standard deviation of 192. During the March-August period, participants consumed a mean of XXXXXXXXXXcalories daily with a standard deviation of 245. The population standard deviations of daily calories consumed for females in the two periods can be estimated using the sample standard deviations, as the samples that were used to compute them were quite large. Construct a 90% confidence interval for μ1 - μ2, the difference between the mean daily calorie consumption μ1 of females in September-Fe
uary and the mean daily calorie consumption μ2 of females in March-August. Then complete the table below. Ca
y your intermediate computations to at least three decimal places. Round your answers to at least two decimal places.
What is the lower limit of the 90% confidence interval?
What is the upper limit of the 90% confidence interval?
3. Below are four bivariate data sets and the scatter plot for each. (Note that each scatter plot is displayed on the same scale.) Each data set is made up of sample values drawn from a population.
Answer the following questions. The same response may be the co
ect answer for more than one question.
1. Which data set is there evidence of strong nonlinear relationship between the two variables? (a) The x, y data set (b) u, v data set (c) w, t, data set (d) the m, n data set (e) NONE
2. Which data set indicates the strongest negative linear relationship between its two variables? (a) The x, y data set (b) u, v data set (c) w, t, data set (d) the m, n data set
3.Which data set indicates a perfect positive linear relationship between its two variables? (a) The x, y data set (b) u, v data set (c) w, t, data set (d) the m, n data set
4. Which data set has an apparent positive, but not perfect, linear relationship between its two variables? (a) The x, y data set (b) u, v data set (c) w, t, data set (d) the m, n data set
4. Below are bivariate data giving birthrate and life expectancy information for each of twelve countries. For each of the countries, both the number of births x per one thousand people in the population and the female life expectancy y (in years) are given. These data are displayed in the Figure 1 scatter plot. Also given are the products of the birthrates and female life expectancies for each of the twelve countries. (These products, written in the column labelled "xy," may aid in calculations.)
Answer the following. Ca
y your intermediate computations to at least four decimal places, and round your answer as specified below.
What is the value of the sample co
elation coefficient for these data? Round your answer to at least three decimal places.
5.
Ca
y your intermediate computations to at least three decimal places and round your answers as specified in the table.