Question

Use the confidence level and sample data to find a confidence interval for estimating the population mean, . Round your answer to the same number of decimal places as the sample mean.

Test scores: n = 175, x¯¯¯=81
, σ=11.8
, 98% confidence

ANSWER CHOICES

A.(77, 85)


B.(79, 83)


C.(76, 86)


D.(72, 90)

Answer 1

Explanation:

We can use the formula for a confidence interval for the population mean:

CI = x¯¯¯ ± z*(σ/sqrt(n))

where:

x¯¯¯ is the sample mean, which is 81.

σ is the population standard deviation, which is 11.8 (assuming the sample is drawn from a normally distributed population).

n is the sample size, which is 175.

z is the z-score corresponding to the desired level of confidence, which is 2.33 for a 98% confidence level.

Substituting the known values, we get:

CI = 81 ± 2.33*(11.8/sqrt(175))

Calculating this expression, we get:

CI ≈ (79, 83)

Therefore, a 98% confidence interval for the population mean is approximately (79, 83).

Therefore, the answer is (B) (79, 83).