Chapter 6, Section 2-CI, Exercise 081 | Use the t-distribution to find a confide

Question

Chapter 6, Section 2-CI, Exercise 081 | Use the t-distribution to find a confidence interval for a mean given the relevant sample results. Give the best point estimate for the margin of error, and the confidence interval. Assume the results come from a random sample from a population that is approximately normally distributed. A 95% confidence interval for using the sample results X-13.5, s = 66, and n-30 Round your answer for the point estimate to cne decimal place, and your answers for the margin of error and the confidence interval to two decimal places point estimate margin of error = The 95% confidence interval is to Click if you would like to Show Work for this question: Open Show Work n the Paint Potential Palie hv vour instructor

Explanation / Answer

Solution:

We are given

Xbar = 13.5

S = 6.6

N = 30

Confidence level = 95%

Point estimate for µ = Xbar = 13.5

Margin of error = t*S/sqrt(n)

Degrees of freedom = n – 1 = 30 – 1 = 29

Critical value = t = 2.0452

Margin of error = 2.0452*6.6/sqrt(30)

Margin of error = 2.0452*1.204989627

Margin of error = 2.4645

Margin of error = 2.46

Confidence interval = Point estimate -/+ Margin of error

Confidence interval = 13.5 -/+ 2.46

Lower limit = 13.5 – 2.46 = 11.04

Upper limit = 13.5 + 2.46 = 15.96

The 95% confidence interval is 11.04 to 15.96.

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