Answer to Question #260650 in Statistics and Probability for Dennis

Question

The lengths (in minutes) of a random selection of popular children’s animated films are listed below. Estimate the true mean length of all children’s animated films with 95% confidence.

91 85 77 94 80 90 78 100 78 76

a. Sample mean:

b. Sample standard deviation:

c. Margin of error:

d. Confidence interval: __________ < mu< __________

Answer 1

a. Sample mean:

$\mu = \frac{91+85+...+78+76}{10} = 84.9$

b. Sample standard deviation:

$s = \sqrt{\frac{(91-84.9)^2 +(85-84.9)^2 +….+(78-84.9)^2 +(76-84.9)^2}{10-1}} = 8.399$

c. Margin of error $= Z_c \times s$

$ME = 1.96 \times 8.399 = 16.46$

d. Confidence interval: 84.9 – 16.46 < mu< 84.9 +16.46

68.44 < mu < 101.36