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 $38 and standard deviation of $2. Construct a confidence interval at a 99% confidence level.

Give your answers to one decimal place.

±

Answer 1

Solution :

Given that,

Point estimate = sample mean = = $38

sample standard deviation = s = $2

sample size = n = 11

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

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2,df = t0.005,10 = 3.169

At 99% confidance level of is

t/2,df * (s /n)

38 3.169 * (2 / 11)

38 1.9