The weight loss franchise home office wanted to compare the results of two centres.A centre in the city provided a weight loss for 152 out of 200 participants.A centre in the suburb provided a weight loss for 109 out of 140 participants.Construct a 98% confidence interval for the difference in the proportions of participants in the city weight loss centre and suburban weight loss centre.

Question

Quizplus · Accepted Answer

The correct confidence interval can be calculated using the formula for the difference in proportions. Given the data, the proportions for the city and suburb centers are 152/200 and 109/140, respectively. Using a 98% confidence level requires a Z-score that corresponds to the confidence level (approximately 2.33 for 98%). The calculation involves the sample proportions, sample sizes, and the Z-score, leading to the interval (-0.1263, 0.0891). This interval suggests that, with 98% confidence, the difference in success rates between the two centers falls within this range.

The Weight Loss Franchise Home Office Wanted to Compare the Results