Question

A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a random sample of 12 apple juice varieties and recorded the density, in pounds per cubic inch, and the percent concentration of each apple juice variety. The scientist wants to estimate the mean change in the density, in pounds per cubic inch, for each increase of 1 percent concentration of apple juice. Assuming the conditions for inference have been met, which of the following inference procedures is most appropriate for this investigation?

a. A linear regression t-interval for slope.
b. A matched-pairs t-interval for a mean difference.
c. A two-sample t-interval for a difference between means.
d. A one-sample t-test for means.
e. A two-sample z-interval for a difference between proportions

Answer 1

The most appropriate inference procedure for this investigation is a linear regression t-interval for slope.

Step-by-step explanation:

The most appropriate inference procedure for this investigation is a linear regression t-interval for slope.

Linear regression is used to analyze the relationship between two variables, in this case, percent concentration and density. The slope of the regression line represents the change in the density for each increase of 1 percent concentration. By conducting a linear regression t-interval for slope, the scientist can estimate the mean change in density and determine if percent concentration can be used to predict density.

This procedure is suitable because the scientist wants to investigate the relationship between two continuous variables (percent concentration and density) and estimate the mean change in density.

Answer 2

The most appropriate inference procedure for the investigation is;

a. A linear regression t-interval for the slope

Step-by-step explanation:

Given that the slope of an horizontal line is zero, we have that there is no change in the y (dependent) variable when there is a change in the x-variable, therefore, it is important to find the true relationship between the two variables, 'x', and 'y'

The confidence interval of the slope is calculated and analyzed to determine if it excludes or includes, 0, such that, if the confidence interval exclude 0, then, it is unlikely that the slope is 0, therefore, there the relationship between the variables, 'x', and 'y' is significant

Therefore, a linear regression t-interval for the slope is most appropriate.