Question

A random sample of 654 women aged 20 to 29 had a mean body mass index (BMI) of 26.8 and a standard deviation of 7.42. Compute a 90% confidence interval for the mean BMI of young women.

Options:
A) 25.912 < μ < 27.687
B) 26.322 < μ < 27.277
C) 25.638 < μ < 27.961
D) 26.124 < μ < 27.776

Answer 1

Using the sample mean, standard deviation, and size provided, and the Z-score for a 90% confidence level, we calculated the 90% confidence interval for the mean BMI of young women to be 26.324 < μ < 27.276, which corresponds to Option B) 26.322 < μ < 27.277.

The correct option is B.

Step-by-step explanation:

The student is asking how to calculate a 90% confidence interval for the mean BMI of young women, using the sample mean of 26.8, sample standard deviation of 7.42, and a sample size of 654. To calculate the confidence interval, we use the formula for a confidence interval of a mean, which is:

μ = α +/- (Z*(σ/√n))

Where μ is the sample mean, Z is the Z-score associated with the confidence level (in this case, the Z-score for a 90% confidence interval is approximately 1.645), σ is the standard deviation, and n is the sample size. Plugging in the values we have:

26.8 +/- (1.645*(7.42/√654))

Calculating the margin of error:

1.645*(7.42/√654) ≈ 0.476

Now we can find the interval:

26.8 - 0.476 < μ < 26.8 + 0.476

So, the 90% confidence interval is:

26.324 < μ < 27.276

Therefore, the correct answer is Option B) 26.322 < μ < 27.277.

The correct option is B.