Question

In a survey, 11 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 $2. Find the margin of error at a 98% confidence level.

Give your answer to two decimal places.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $46

sample standard deviation = s = $2

sample size = n = 11

Degrees of freedom = df = n - 1 =11-1=10

At 98% confidence level the t is ,

= 1 - 98% = 1 - 0.98 = 0.02

/ 2 = 0.02 / 2 = 0.01

t /2,df = t0.01,10 = 2.764

Margin of error = E = t/2,df * (s /n)

= 2.764 * (2 / 11)

Margin of error = E = 1.67