Question

A major food manufacturer is concerned that the sales for its skinny french fries have been decreasing. As a part of a feasibility study, the company conducts research into the types of fries sold across the country to determine if the type of fries sold is independent of the area of the country. The results of the study are shown in Table $11.48$. Conduct a test of independence.

Short answer

(a) Null hypothesis, $H_0$:Thetypesoffriessoldareindependentofthelocation

(b) Alternate hypothesis $H_a$: Thetypesoffriessoldaredependentonthelocation

(c) Degree of freedom $df=6$

(d) Distribution is ${x_6}^2$

(e)

Test statistic for independent test ,

Test statistic = $18.84$

(f) P - value

(g) Chi square graph,

(h)

i. $0.05$is the alpha value.

ii. Decision is that, the null hypothesis must be rejected.

iii. Reason for the decision:$p$value $<$alpha.

iv. Conclusion: There is substantial evidence that types of fries and location are linked at the $5\%$significant level.

Step-by-step solution

Part (a) Step 1: Given information

Given that, carry out an independence test.

Explanation

Null hypothesis $H_0$is Thetypesoffriessoldareindependentofthelocation.

Part (b) Step 1: Given information

Given that, conduct a test of independence.

Explanation

Alternate hypothesis $H_a$is Thetypesoffriessoldaredependentonthelocation

Part (c) Step 1: Given Information

Given that, conduct a test of independence.

Explanation

Degree of freedom ,

$$\begin{gathered} df=(4-1)(3-1) \\ df=6 \end{gathered}$$

Part (d) Step 1: Given information

Given that, to conduct a test of independence.

Explanation

Test distribution is${x_6}^2$

Part (e) Step 1: Given information

Given that, conduct a test of independence.

Explanation

Calculation:

The independence test statistic is

Test statistic =$18.84$

Part (f) Step 1: Given information

Given that, conduct a test for independence.

Explanation

Calculation for P - value is,

Part (g) Step 1: Given information

Given that, Conduct a test of independence.

Explanation

Below graph is Chi- Square

Part (h) Step 1: Given information

Given that, conduct a test of independence.

Explanation

i. $0.05$is the alpha value.

ii. Decision is that, the null hypothesis must be rejected.

iii. Reason for the decision is$P$-value$<$alpha.

iv. Conclusion: There is substantial evidence that types of fries and location are linked at the $5\%$significant level.