In a simple random sample of 100 women from Richmond, Virginia, the average amount of money that these women spent per visit at their hair salons is $32.43. The standard deviation from this sample is $7.84.
Which of these is an approximate 95% confidence interval for the mean amount of money that all women in Richmond spend per visit at their hair salons?
A) $32.43 ± $0.784
B) $32.43 ± $1.568
C) $32.43 ± $7.84
D) $7.84 ± $3.243
E) $7.84 ± $6.486

Question

Quizplus · Accepted Answer

To find the 95% confidence interval, we can use the formula:

CI = X̄ ± Z*(σ/√n)

where X̄ is the sample mean, σ is the standard deviation, n is the sample size and Z is the Z-score for the level of confidence.

For a 95% confidence interval, Z = 1.96.

Plugging in the values from the sample, we get:

CI = 32.43 ± 1.96*(7.84/√100)

Simplifying this expression, we get:

CI = 32.43 ± 1.568

Therefore, the approximate 95% confidence interval is $32.43 ± $1.568, which is answer choice B.

In a Simple Random Sample of 100 Women from Richmond