Question

You have data that indicates that people who followed a particular exercise regimen ended up losing weight and being healthier overall. In fact, out of 363 people in a study, the average weight lost under the regimen was 12 pounds with a standard deviation of 5 pounds. Please fill in the blank: You can be 99% sure that a random person who followed the exercise regimen will lose at least _____________ pounds.

a) 11.39

b) 11.31

c) 0.35

d) -0.88 (gaining 0.88 pounds)

e) Answer is not there

Answer 1

The provided sample mean is 12 and the sample standard deviation is s = 5. The size of the sample is n = 363 and the required confidence level is 99%.

The number of degrees of freedom are df = 363 - 1 = 362 , and the significance level is \alpha = 0.01α=0.01.

Based on the provided information, the critical t-value for α=0.01 and df = 362 degrees of freedom is t_c = 2.589

The 99% confidence for the population mean μ is computed using the following expression

Therefore, based on the information provided, the 99 % confidence for the population mean μ is

Since, the lower limit of the interval is 11.31

hence,  the exercise regimen will lose at least 11.31 pounds.