Question

In a survey, 28 people were asked how much they spent on their child's last birthday gift. The results were roughly shaped as a normal curve with a mean of $39 and standard deviation of $2. Find the margin of error at a 90% confidence level.

Give your answer to two decimal places.

m =

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 39

sample standard deviation = s = 2

sample size = n = 28

Degrees of freedom = df = n - 1 = 28 - 1 = 27

At 90% confidence level

= 1 - 90%

=1 - 0.90 =0.10

/2 = 0.05

t/2,df = t0.05,27 = 1.703

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

= 1.703 * (2 / 28)

Margin of error = E = 0.64