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, 371 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 137 die-hard fans, 89.8% reported that they had watched or listened to Cubs games when they were children. Among the 234 less loyal fans, 68.4% 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.)

_____ 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.)

(c) Express the results with a 95% confidence interval for the difference in proportions. (Round your answers to three decimal places.)

(______, _______)

_____ 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.)

Explanation / Answer

a)numbers of die-hard Cubs fans who watched or listened to games when they were children=137*0.898=123.02~123

numbers of less loyal fans who watched or listened to games when they were children= 234*0.684=160.053~160

here p1 =0.898 ' n1=137

p2=0.684 ; n2=234

hence std error =(p1(1-p1)/n1+p2(1-p2)/n2)1/2 =0.0399

hence test stat z=(p1-p2)/std error =5.363

p value=0.0000

c) for 95% CI, z=1.96

hence confidence interval =(p1-p2)+/- z*std error =0.136 ; 0.292

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