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

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.

we know that

the area of the composite figure is equal to the area of a rectangle plus the area of a triangle

see the attached figure to better understand the problem

step 1

find the area of the rectangle

we know that the area of a rectangle is equal to

where

b is the base of the rectangle

h is the height of the rectangle

in this problem we have

substitute

step 2

find the area of the triangle

we know that the area of the triangle is equal to

where

b is the base of the triangle

h is the height of the triangle

in this problem we have

substitute

step 3

find the area of the composite figure

the area of the composite figure is equal to the area of a rectangle plus the area of a triangle

therefore

the answer is the option