4. A study was done on the accuracy of newspaper advertisements by the five type

Question

4. A study was done on the accuracy of newspaper advertisements by the five types of food stores in a city. On each of 4 days, items were randomly selected from the advertisements for each type of store and the actual price was compared to the advertised price. Each of the stores in the city was classified as one of the following types: nation chain, regional chain A, regional chain B, regional chain C, or independent. Values in the table represent the number of items that were correctly and incorrectly priced. Type of Store nation chain regional chain A regional chain B regional chain C Independent Number correctly priced 89 53 43 32 41 Number incorrectly priced 10 14 12 13 Determine whether these data provide sufficient evidence to conclude that the proportion of correctly price items for stores of National chain is higher than that of the regional Chain A. Use the significance level 0.10. Test whether the data provide sufficient evidence to conclude that the proportion of correctly priced items are the same for the five types of stores. Use significance level 0.05, a. b. Use a 95% confidence interval to estimate the proportion ofcorrectly priced items in the stores in the national chain category

Explanation / Answer

a) Here, we can consider the following testing problem,

H0 : proportion of correctly priced items for stores of National chain is same as that of regional chain A

against

H1 : proportion of correctly priced items for stores of National chain is greater than that of regional chain A

Here, we have to test for the two sample proportions

I used R code to solve this problem and by calculation the p-value for this test at 10% level of significance is coming out to be, p-value = 0.04314 which is less than 0.1 and hence we can conclude on the basis of the given data at 10% level of significance that proportion of correctly priced items for stores of National chain is greater than that of regional chain A.

R Code: prop.test(c(89,53),c(99,67),alternative = "greater",conf.level = 0.9)

b) Here, we want to test the following problem,

H0 : the proportion of correctly priced items are same for all the five type of stores  

against

H1 : the proportion of correctly priced items are not the same for all the five type of stores

I used R code to solve this problem and by calculation the p-value for this test at 5% level of significance is coming out to be, p-value = 0.05714 which is greater than 0.05 and hence we can conclude on the basis of the given data at 5% level of significance that the proportion of correctly priced items are same for all the five type of stores.

R Code: prop.test(c(89,53,43,32,41),c(99,67,55,45,48),alternative = "two.sided",conf.level = 0.95)

c) The 95% confidence interval for the National chain category store is coming out to be, (0.8179215, 0.9478398) [I used R code here too]

R Code: prop.test(89,99,alternative = "two.sided",conf.level = 0.95)

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