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. Conduct a test of independence. Assume α = 0.05. Type of Fries Northeast South Central West Skinny Fries Expected 68 66 83 72 Curly Fries Expected 51 89 73 89 Steak Fries Expected 94 94 81 66 Calculate the expected frequencies for each entry in the table above and enter them below the observed values in the table above. [Round your answer to 3 decimal places.] State the null and the alternative hypotheses: H 0 = The types of fries sold are H 1 = The types of fries sold are Identify the claim: Identify the distribution to use for the test: . The degrees of freedom: . Compute the test statistic. Test Statistic = [Round your answer to 4 decimal places.] What is the p-value? p-value = [Round your answer to 4 decimal places.] Indicate the correct decision and state appropriate conclusions. Significance level, α: Decision: Reason for decision: Conclusion of the hypothesis test: There is evidence at 5% level of significance to the claim that the types of fries sold are

Answer 1

We have,

Original (Oi)	Skinny Fries	Curly Fries	Steak Fries	Total
North East	68	51	94	213
South	66	89	94	249
Central	83	73	81	237
West	72	89	66	227
Total	289	302	335	926

The expected values are given by

Hence, we get the expected frequencies-

Expected (Ei)	Skinny Fries	Curly Fries	Steak Fries	Total
North East	66.476	69.467	77.057	213
South	77.712	81.207	90.081	249
Central	73.966	77.294	85.740	237
West	70.846	74.032	82.122	227
Total	289	302	335	926

  H₀ = The types of fries sold are independent of the area of the country. (Claim)

H₁ = The types of fries sold are not independent of the area of the country.

We will use chi-square test for this problem.

The degrees of freedom are given by

df= (number of rows- 1)(number of columns- 1)= 6

The test statistics is given by-

The p-value is given by

Significance level, α: 0.05

Decision: Reject H₀.

Reason for decision: P-value is less than significance level

Conclusion of the hypothesis test: There is evidence at 5% level of significance to the claim that the types of fries sold are independent of the area of the country.