According to literature on brand loyalty, consumers who are loyal to a brand are

Question

According to literature on brand loyalty, consumers who are loyal to a brand are likely to consistently select the same product. This type of consistency could come from a positive childhood association. To examine brand loyalty among fans of the Chicago Cubs, 370 Cubs fans among patrons of a restaurant located in Wrigleyville were surveyed prior to a game at Wrigley Field, the Cubs' home field. The respondents were classified as "die-hard fans" or "less loyal fans." Of the 131 die-hard fans, 93.1% reported that they had watched or listened to Cubs games when they were children. Among the 239 less loyal fans, 68.2% said that they watched or listened as children. (Let D = pdie-hard pless loyal.) (a) Find the numbers of die-hard Cubs fans who watched or listened to games when they were children. Do the same for the less loyal fans. (Round your answers to the nearest whole number.) die-hard fans less loyal fans (b) Use a one sided significance test to compare the die-hard fans with the less loyal fans with respect to their childhood experiences relative to the team. (Use your rounded values from part (a). Use = 0.01. Round your z-value to two decimal places and your P-value to four decimal places.) z = P-value =

Explanation / Answer

(a) Find the numbers of die-hard Cubs fans who watched or listened to games when they were children. Do the same for the less loyal fans.

ANswer :  numbers of die-hard Cubs fans who watched or listened to games when they were children = 131 * 93.1/100 = 122

numbers of less loyal fans who watched or listened to games when they were children = 239 * 68.2/100 = 163

Number of loyal fans less die hard cubs = 163 - 122 = 41

(b) one sided significance test with the less loyal fans with respect to their childhood experiences relative to the team.

H0 : pdie-hard = pless royal

Ha : pdie-hard > pless royal

Pooled estimate p = (163 + 122)/ 370 = 0.77

Standard error of pooled estimate se0 = sqrt [p(1-p) (1/n1 + 1/n2 )] = sqrt [ 0.77 * 0.23 * (1/131 + 1 /239) ] = 0.0457

so Test Statistic

Z =  (pdie-hard - pless royal )/ se0 = (0.931 - 0.682)/0.0457 = 5.45

for alpha = 0.01 the critical Z - value = 2.33

so P - value = 0.00001 so we can reject the null hypothesis

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.