It is known that the standard deviation for the number of minutes women spend applying makeup everyday is 17 minutes if you want to construct a 95% confidence interval for the mean amount of time women spend applying make up with a margin of error of no more than 5 mins. At least how many women must you survey

95% = mean ± 1.96SEm

1.96 SEm ≤ 5

SEm = SD/√n

I'll let you do the calculations.

To determine the minimum sample size required, we need to consider the formula for the sample size calculation of a confidence interval:

n = (Z * σ / E) ^ 2

Where:
- n is the sample size
- Z is the Z-score corresponding to the desired level of confidence (in this case, for a 95% confidence level, Z ≈ 1.96)
- σ is the standard deviation of the population (17 minutes in this case)
- E is the maximum margin of error allowed (5 minutes in this case)

Substituting the given values into the formula:

n = (1.96 * 17 / 5) ^ 2

n ≈ (33.32 / 5) ^ 2

n ≈ 6.664 ^ 2

n ≈ 44.351296

Since the sample size must be a whole number, we round up to the nearest whole number:

n ≈ 45

Therefore, at least 45 women must be surveyed to construct a 95% confidence interval for the mean amount of time women spend applying makeup, with a margin of error no more than 5 minutes.