A business professor conducted a campus survey to estimate demand among all students for a protein supplement for smoothies and other nutritional drinks. Each of 113 students, randomly
Selected from all students on campus, provided the following information: (1) How health conscious are you? (Very, Moderately, Slightly, Not very)
(2) Do you prefer protein supplements in your smoothies? (Yes, No)
As part of his analysis, the professor claims that whether or not the student prefers a protein supplement in smoothies is independent of health consciousness level (Very, Moderate, Slightly, or Not very). Use the chi-square distribution to determine the rejection region for this test when testing at $\alpha = 0.05$.
A) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } 5.99147$
B) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } 9.48773$
C) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } 7.81473$
D) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } 9.34840$

Question

A business professor conducted a campus survey to estimate demand among all students for a protein supplement for smoothies and other nutritional drinks. Each of 113 students, randomly
Selected from all students on campus, provided the following information: (1) How health conscious are you? (Very, Moderately, Slightly, Not very)
(2) Do you prefer protein supplements in your smoothies? (Yes, No)
As part of his analysis, the professor claims that whether or not the student prefers a protein supplement in smoothies is independent of health consciousness level (Very, Moderate, Slightly, or Not very). Use the chi-square distribution to determine the rejection region for this test when testing at $\alpha = 0.05$.
A) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 5.99147$
B) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 9.48773$
C) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 7.81473$
D) Reject $\mathrm { H } _ { 0 }$ if $\chi ^ { 2 } > 9.34840$

Quizplus · Accepted Answer

The chi-square test for independence has degrees of freedom calculated as $(r-1)(c-1)$, where $r$ is the number of rows and $c$ is the number of columns in the contingency table. Here, we have 4 levels of health consciousness (rows) and 2 preferences for protein supplements (columns), so the degrees of freedom are $(4-1)(2-1) = 3$. For a significance level of $\alpha = 0.05$ and 3 degrees of freedom, the critical value from the chi-square distribution table is approximately 7.81473.

A Business Professor Conducted a Campus Survey to Estimate Demand α=0.05\alpha = 0.05α=0.05

A Business Professor Conducted a Campus Survey to Estimate Demand $\alpha = 0.05$