Question

Probability and Confidence Intervals Emily is trying to select a weight-loss plan to follow. She has narrowed her decision down to two different weight-loss plans. Recall the following formula for finding a confidence interval: Both weight loss plans make the following claim: Use the formula to find a confidence interval for the true percentage of participants who lost at least 10 pounds in the first month using each plan. "Fifty-eight percent of participants lost at least 10 pounds in the first month." Emily decides to dig further. She reviews the studies conducted by both companies and finds the following information on the amount of weight lost by participants in the first month of following the weight loss plan. Confidence interval for Plan A: Confidence interval for Plan B: Plan A Plan B Which plan should Emily choose? Use your confidence intervals to explain your answer. Lost less than 2 lbs 2 1 Lost 2-4 lbs 0 1 Lost 4-6 lbs 1 2 Lost 6-8 lbs 2 25 Lost 8-10 lbs 0 10 Lost over 10 lbs 7 53 Total Number of participants 12 92

Answer 1

From the data we find the 95% confidence interval for the two plans.

Plan A

7 out of 12 lost more than 10 kg.
p = 7/12 = 0.583333333

The confidence interval is given below.

Plan B

53 out of 92 lost more than 10 kg.
p = 53/92 = 0.576086957

The confidence interval is given below.

Hence for plan B, the true mean proprotion of the population losing more than 10 kgs much higher than plan A. Hence plan B is better plan.

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