the claimed value for several groups of one categorical variable using the chi-squared test for goodness of fit. Company A has recently conducted aggressive advertising campaigns to maintain and possible increase its share of the market for fabric softener. Its main competitor, company B, has 39% of the market, and a few other competitors account for the remaining 19%. To determine whether the market shares changed after the advertising campaign, the marketing manager for company A solicited the preferences of a random sample 220 customers of fabric softener. Of the 220 customers, 99 indicated a preference for company A's product, 80 preferred company B's product, and the remaining 41 preferred the products of one of the other competitors. Can the analyst infer at 4% significance level that customer preferences have changed from their levels before the advertising campaigns were launched? a. The chi-squared test for goodness of fit is used to answer this question because Othere are numerical (or quantitative) variables. O there are several proportions (or counts) of one categorical (or qualitative) variable to compare Othere are two categorical (or qualitative) variables to test for independence. b. Selct the correct statement for the null hypothesis (Ho) of this chi-squared test for goodness of fit. O At least one proportion is different from the claimed proportion (There is a change in customer preferences after the advertising campaign) OP₁ = 0.42, P2 = 0.39, p3= 0.19; All the proportions are equal to the claimed proportions (There is no change in customer preferences after the advertising campaign) O not all proportions are same (at least one proportion is different; there is a difference in customer preferences among companies) P1 = P2 = P3 = 1/3; All the proportions are equal (There is no difference in proportion of customer preferences among companies)
the claimed value for several groups of one categorical variable using the chi-squared test for goodness of fit. Company A has recently conducted aggressive advertising campaigns to maintain and possible increase its share of the market for fabric softener. Its main competitor, company B, has 39% of the market, and a few other competitors account for the remaining 19%. To determine whether the market shares changed after the advertising campaign, the marketing manager for company A solicited the preferences of a random sample 220 customers of fabric softener. Of the 220 customers, 99 indicated a preference for company A's product, 80 preferred company B's product, and the remaining 41 preferred the products of one of the other competitors. Can the analyst infer at 4% significance level that customer preferences have changed from their levels before the advertising campaigns were launched? a. The chi-squared test for goodness of fit is used to answer this question because Othere are numerical (or quantitative) variables. O there are several proportions (or counts) of one categorical (or qualitative) variable to compare Othere are two categorical (or qualitative) variables to test for independence. b. Selct the correct statement for the null hypothesis (Ho) of this chi-squared test for goodness of fit. O At least one proportion is different from the claimed proportion (There is a change in customer preferences after the advertising campaign) OP₁ = 0.42, P2 = 0.39, p3= 0.19; All the proportions are equal to the claimed proportions (There is no change in customer preferences after the advertising campaign) O not all proportions are same (at least one proportion is different; there is a difference in customer preferences among companies) P1 = P2 = P3 = 1/3; All the proportions are equal (There is no difference in proportion of customer preferences among companies)
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Chi-Squared Test for Goodness of Fit: Analyzing Advertisement Impact on Market Shares**
**Objective:**
The goal is to test whether population proportions are equal to the claimed value for several groups of one categorical variable using the chi-squared test for goodness of fit.
**Scenario:**
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 39% of the market, and a few other competitors account for the remaining 19%.
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 220 customers of fabric softener.
Of the 220 customers, 99 indicated a preference for company A's product, 80 preferred company B's product, and the remaining 41 preferred the products of one of the other competitors.
**Research Question:**
Can the analyst infer at a 4% significance level that customer preferences have changed from their levels before the advertising campaigns were launched?
### Analysis:
**a. The Chi-Squared Test for Goodness of Fit**
The chi-squared test for goodness of fit is used to answer this question because:
- **Option 2:** There are several proportions (or counts) of one categorical (or qualitative) variable to compare.
**b. Null Hypothesis Selection (H0):**
Select the correct statement for the null hypothesis (H0) of this chi-squared test for goodness of fit:
- **Option 2:** \( p1 = 0.42, p2 = 0.39, p3 = 0.19 \); All the proportions are equal to the claimed proportions (There is no change in customer preferences after the advertising campaign).
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