Company A has recently conducted aggressive advertising campaigns to maintain an

Question

Company A has recently conducted aggressive advertising campaigns to maintain and possibly increase its share of the market for fabric softener. Its main competitor, company B, has 35% of the market, Company C has 18% of the market, and a number of other competitors account for the remaining 10%. To determine whether the market shares changed after the advertising campaign, the marketing manager for company A solicited the preferences of a random sample of 200 customers of fabric softener. Of the 200 customers, 97 indicated a preference for company A’s product, 55 preferred company B’s fabric softener, 32 indicated a preference for company C’s product, and the remaining 16 preferred the products of one of the competitors. Can the analyst infer at the 2% significance level that customer preferences have changed from their levels before the advertising campaigns were launched? Do a complete and appropriate hypothesis test, using Excel, the 5step procedure discussed in class, and the pvalue approach. If and only if it is appropriate to do so, offer one informal comment as to where the single largest difference is.

please use mega stat

Explanation / Answer

here observed(O) frequency is number of customer after campaigning and Expected (E) frequency is number of customer before campaigning

here null hypothesis H0: observed=expected

alternate hypotheis Ha:observed is not equal to expected

level of significance alpha=0.02

we use chi-square test and chi-square=sum((O-E)2)/E =11.61 with k-1=4-1=3 df

p-value=0.0088 is less than alpah=0.05 so we reject null hypothesis and conclude that customer preferences have changed from their levels before the advertising campaigns were launched.

( critical chi-square(0.02,3)=9.84 is less than calcuated chi-square=11.61, so we reject null hypothesis)

company % share Observed(O) Expected(E) (O-E) (O-E)2/E A 37 97 74 23 7.15 B 35 55 70 -15 3.21 C 18 32 36 -4 0.44 other 10 16 20 -4 0.80 Total 100 200 200 0 11.61

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