Question

In a survey, 23 people were asked how much they spend on their child’s last birthday gift. The results were roughly bell-shaped with a mean of $37 and standard deviation of $2. Find the margin of error at an 80% confidence level. Find the confidence interval and give a complete confidence statement. Round to 2 decimal places.

Answer 1

solution :

Given that,

Point estimate = sample mean = = 37

sample standard deviation = s = 2

sample size = n = 23

Degrees of freedom = df = n - 1 = 23 - 1 = 22

At 80% confidence level

= 1 - 80%

=1 - 0.80 = 0.20

/2 = 0.10

t/2,df = 1.321

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

= 1.321 * (2 / 23)

Margin of error = E = 0.55