Question

a) If n=10, ¯xx¯(x-bar)=33, and s=10, construct a confidence interval at a 80% confidence level. Assume the data came from a normally distributed population.

Give your answers to one decimal place.

< μμ <

b) In a survey, 27 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $46 and standard deviation of $8. Find the margin of error at a 99% confidence level.

Give your answer to two decimal places.

c) If n=29, ¯xx¯(x-bar)=36, and s=8, find the margin of error at a 90% confidence level

Give your answer to two decimal places.

Answer 1

a)

80% Confidence Interval
X̅ ± t(α/2, n-1) S/√(n)
t(α/2, n-1) = t(0.2 /2, 10- 1 ) = 1.383
33 ± t(0.2/2, 10 -1) * 10/√(10)
Lower Limit = 33 - t(0.2/2, 10 -1) 10/√(10)
Lower Limit = 28.6
Upper Limit = 33 + t(0.2/2, 10 -1) 10/√(10)
Upper Limit = 37.4

28.6 < < 37.4

b)

t critical value at 0.01 significance level with 26 df = 2.779

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

= 2.779 * 8 / sqrt(27)

= 4.28

c)

t critical value at 0.1 significance level with 28 df = 1.701

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

= 1.701 * 8 / sqrt(29)

= 2.53