Question

A scientist selected a random sample of seven varieties of peach ice cream to investigate the relationship between the density, in pounds per cubic inch, of the varieties of ice cream and the percent concentration of peaches in the ice cream. Assuming all conditions for inference are met, which of the following significance tests should be used to investigate whether there is convincing evidence at the 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream?

A. A two-sample t-test for a difference between means

B. A chi-square test of independence

C. A linear regression t-test for slope

D. A two-sample z-test for a difference between proportions

E. A matched pairs t-test for a mean difference

Answer 1

The significance test that would be used to investigate whether there is convincing evidence at 0.05 level of significance that a greater percent of peaches in the ice cream is associated with an increase in the density of the ice cream is option C;

C. A linear regression t-test for slope

Explanation:

The linear regression t-test for slope is a test for determining the existence of a statistically significant linear relationship between two variables, a independent variable, X and an dependent variable Y in the following form;

Y = B₀ + B₁·X

The test is used to test the regression line slope where we have;

B₀ = The constant

B₁ = The slope also known as the regression coefficient

The given information tested in the question is if an increase in the peaches in the ice cream is associated with an increase in the density of the ice cream, therefore, the test to investigate the relationship between the rate of both variables is the linear regression t-test for slope.

Therefore, we have

Y = B₀ + B₁·X

Where;

X = The percentage of peaches in the ice cream

Y = The density of the ice cream