Question

The lengths (in minutes) of a random selection of eleven popular children’s animated films are listed below. The data listed below may or may not normally distributed, how can you tell if the data is approximately normally distributed? (hint median and mean) Construct a confidence interval estimate for the true mean length of all children’s animated films with 98% confidence. 93, 83, 76, 91, 77, 82 ,78, 95, 82 ,70, 75

State the Margin of Error, Best point estimate and Include the written statement.

State how you would know if this Data is normally distributed?

Please list all work.

Answer 1

Confidence interval for Population mean is given as below:

Confidence interval = Xbar ± t*S/sqrt(n)

From given data, we have

Best point estimate = Xbar = 82

S = 8.01249025

n = 11

df = n – 1 = 10

Confidence level = 98%

Critical t value = 2.7638

(by using t-table)

Confidence interval = Xbar ± t*S/sqrt(n)

Confidence interval = 82 ± 2.7638*8.01249025/sqrt(11)

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

Margin of error = 2.7638*8.01249025/sqrt(11)

Margin of error = 6.6769

Confidence interval = 82 ± 6.6769

Lower limit = 82 - 6.6769 = 75.32

Upper limit = 82 + 6.6769 = 88.68

Confidence interval = (75.32, 88.68)