128k views
0 votes
If X=74, o=9, and n=60, construct a 95% confidence interval
estimate of the population mean

User Jackpot
by
7.5k points

1 Answer

2 votes

Final answer:

To construct a 95% confidence interval for the population mean with X=74, o=9, and n=60, calculate the standard error, multiply by the Z-score for 95% (1.96), and add/subtract from the sample mean to get the interval, which is (71.722, 76.278).

Step-by-step explanation:

To construct a 95% confidence interval estimate of the population mean when X=74, o=9, and n=60, you can use the formula for the confidence interval of the mean when the population standard deviation is known:

CI = µ ± Z*(σ/√n)

Where µ is the sample mean (X), σ is the population standard deviation (o), n is the sample size, and Z* is the Z-score corresponding to the desired confidence level. For a 95% confidence interval, the Z-score is typically 1.96.

First, calculate the standard error (SE):

SE = o / √n = 9 / √60 = 9 / 7.746 = 1.162

Then, multiply the standard error by the Z-score:

Margin of Error (ME) = Z* × SE = 1.96 × 1.162 = 2.278

Now, find the lower and upper bounds of the confidence interval:

Lower Bound = X - ME = 74 - 2.278 = 71.722

Upper Bound = X + ME = 74 + 2.278 = 76.278

The 95% confidence interval estimate for the population mean is (71.722, 76.278).

User Karthik Sivam
by
8.5k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories