Question

Overeating for just four weeks can increase fat mass and weight over two years later, a Swedish study shows.^1 Researchers recruited 18 healthy and normal-weight people with an average age of 26. For a four-week period, participants increased calorie intake by 70% (mostly by eating fast food) and limited daily activity to a maximum of 5000 steps per day (considered sedentary). Not surprisingly, weight and body fat of the participants went up significantly during the study and then decreased after the study ended. Participants are believed to have returned to the diet and lifestyle they had before the experiment. However, two and a half years after the experiment, the mean weight gain for participants was 6.8 lbs with a standard error of 1.2 lbs. A control group that did not binge had no change in weight.^1 Ernersson, A., Nystrom, F., and Linsstrrom, T., "Long-Term Increase of Fat Mass after a Four Week Intervention with a Fast-Food Hyper-Alimentation and Limitation of Physical Activity, " Nutrition & Metabolism, 2010; 7: 68. Some of the data is estimated from available information. (c) Give a 95% confidence interval for the parameter. Round your answers to one decimal place. The 95% confidence interval for X is ____to _______ (d) Give the margin of error. The margin of error is plusminus _________

Answer 1

Answer: [a] 95% confidence interval = 4.4 < Ẍ <9.2

               [b] margin of error = ± 2.4

Step-by-step explanation:

here let us carefully look into this problem,

from the question, we have that  Ẍ  = 6.8, and SE = 1.2

let us begin

(a). asked to calculate the 95% confidence interval we have;

       95% C.I = Ẍ ±  2 (SE) = 6.8 ±  2(1.2) = 6.8 ±  2.4

        95% C.I = (4.4, 9.2)

this gives the confidence interval to be (4.4 < Ẍ < 9.2).

(b). the error margin is ±  2.4, which implies that our estimate of 6.8 pounds is within 2.4 pounds of the true mean weight gain for the population.

cheers i hope this helped a great deal !!1