D Spring 2017 Commence x H yBoisestate I Welcome x M Spring 2017 Commence omewor
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D Spring 2017 Commence x H yBoisestate I Welcome x M Spring 2017 Commence omework 3B Secure www.webassignn 15441863 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, 374 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 135 die hard fans, 88.1% reported that they had watched or listened to Cubs games when they were children. Among the 239 less loyal fans, 68.6% said that they watched or listened as children (Let D. pdie.ha 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 fan ith respect to their childhood experiences relative to the team. (Use your rounded values from part (a). Use a 0.01. Round your z- value to two decimal places and your P-value to four decimal places.) P-value Conclusion Fail to reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children. Reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children Reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children Fail to reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans watched or listened to Cubs games as children (c) Express the results with a 95% confidence interval for the difference in proportions. (Round your answers to three decimal places.) eBook My Notes o Ask Your Teacher points MIntroStatB 8 E.517 XP. 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, 383 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," The study found that 64.4% of the 132 die-hard fans attended Cubs games at least once a month, but only 19.9% of the 251 less loyal fans attended this often. Analyze these data using a significance test for the difference in proportions. 0.05. Round your value for z to two decimal places. Round your P-value to four decimal Pdie-hard ess loyal places P-value Analyze these data using a 95% confidence interval for the difference in proportions. (Round your answers to three decimal places Write a short summary of your findings Fail to reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month Reject the null hypothesis, there is significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month Reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month Fail to reject the null hypothesis, there is not significant evidence that a higher proportion of die hard Cubs fans attend games at least once a month.Explanation / Answer
11 )
we know that pooled sample proportions is given as
p = (p1 * n1 + p2 * n2) / (n1 + n2) , where p1 is proportion 1 and p2 is proportion 2 , n1 and n2 are the 2 sample sizes , so we use these values to first calculate the pooled sample variance
putting the values
= (0.64*132 +0.199*251)/(251+132) = 0.350
once we have the pooled sample variance , we then use it to calculate the standard error , which is given as the below formula
now standard error SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }
= sqrt((0.35*0.65)*((1/251)+(1/132))) = 0.05 , now we use the SE value to calculate the Z value
and finally The test statistic is a z-score (z) defined by the following equation.
z = (p1 - p2) / SE
= (0.64 - 0.199)/0.05 = 8.8. You must keep the z tables handy with you.
now the p valude from the z table for this would be almost zero. As the p value < 0.05 , hence we can reject null hypothesis
hence we reject null hypothesis and conclude that there is a signifcant evidence that a higher proportion of die hard fans attend games at least once a month
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