A weight loss centre provided a loss for 72% of its participants.The centre's leader decides to test a new weight loss strategy on a random sample size of 140 and found weight loss in 78% of the participants.Create a 95% confidence interval for the proportion of participant weight loss.

A) Based on the data,we are 95% confident the proportion of participant weight loss is between 64.56% and 79.44%.
B) Based on the data,we are 95% confident the proportion of participant weight loss is between 64.56% and 85.44%.
C) Based on the data,we are 95% confident the proportion of participant weight loss is between 57.84% and 98.16%.
D) Based on the data,we are 95% confident the proportion of participant weight loss is between 72% and 84%.
E) Based on the data,we are 95% confident the proportion of participant weight loss is between 71.14% and 84.86%.

Question

Kevin Jackson · Accepted Answer

Final Answer : E, Explanation :  To create a 95% confidence interval for the proportion of participant weight loss, we can use the formula:(sample proportion) +/- (critical value) x (standard error)where the sample proportion is 0.78 (from the information given in the question), the critical value for a 95% confidence level is 1.96 (from a standard normal distribution table), and the standard error can be calculated as:sqrt[(sample proportion x (1 - sample proportion)) / sample size]= sqrt[(0.78 x 0.22) / 140]= 0.043Plugging in the values, we get:0.78 +/- 1.96 x 0.043= 0.78 +/- 0.084Therefore, the 95% confidence interval for the proportion of participant weight loss is between 0.78 - 0.084 = 0.696 (or 69.6%) and 0.78 + 0.084 = 0.864 (or 86.4%).Taking into account the given answer choices, the closest interval to this is answer choice E, where we are 95% confident that the proportion of participant weight loss is between 71.14% and 84.86%.

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