Confidence interval of population mean

Question

1) In a test of the Keto weight loss program, 40 adults used the diet program and after 12 months their mean weight loss was 4.7 lbs, with a sample standard deviation of 3.56 lbs. Construct a 95% confidence interval of the population mean’s weight loss for all participants of the study. Does the Keto diet program appear to be effective, and practical? Explain fully.

Answer 1

The sample size, 40, is greater than 30, so we can assume a normal distribution.

We don't know the population standard deviation. However, we have a sample standard deviation, so we'll use a T-Interval.

TInterval(x: 4.7, Sx: 3.56, n: 40, C-Level: 0.95) ≈ {3.5615, 5.8385}

Because 0 isn't within the interval and all values are greater than 0, the Keto diet program appears to be effective.

Note: In my opinion, losing only 3.5-5.8 pounds in 12 months is very slow, so I would say otherwise to this program being effective and practical in real life.