A random sample of 30 women drank an average of 15 cups of coffee per week during examination finals,

with the sample standard deviation equal to 3 cups. A upper limit of an approximate confidence interval
with 95% of the population average cup drunk is ?

To find the upper limit of an approximate confidence interval for the population average number of cups drunk, we can use the formula:

Upper Limit = Sample Mean + (Critical value * Standard Error)

The critical value is based on the desired confidence level and the sample size. For a 95% confidence level, the critical value is commonly 1.96 for a sample size of 30.

The standard error is calculated by dividing the sample standard deviation by the square root of the sample size.

Let's calculate the upper limit step-by-step:

1. Calculate the standard error:
Standard Error = Sample Standard Deviation / √Sample Size
Standard Error = 3 / √30 ≈ 0.5477

2. Determine the critical value for a 95% confidence level and a sample size of 30. In this case, the critical value is 1.96.

3. Multiply the critical value by the standard error:
Critical Value * Standard Error = 1.96 * 0.5477 ≈ 1.072

4. Add the result from step 3 to the sample mean to find the upper limit:
Upper Limit = Sample Mean + (Critical Value * Standard Error)
Upper Limit = 15 + 1.072 ≈ 16.072

Therefore, the approximate upper limit of the confidence interval with 95% confidence for the population average number of cups drunk is approximately 16.072 cups.

95% confidence interval = μ ± 1.96 SE

Standard Error (SE) = SD/√(n-1)

Z = (x-μ)/SE

1.96 = (x-15)/SE

Solve for x.

I hope this helps.