Question

(1 point) Justin is interested in buying a digital phone. He visited 11 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 166.8 and a standard deviation of 30.8.

(a) What t-score should be used for a 95% confidence interval for the mean, ?μ, of the distribution?
t* =

(b) Calculate a 95% confidence interval for the mean price of this model of digital phone:
(Enter the smaller value in the left answer box.)  

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 166.8

sample standard deviation = s = 30.8

sample size = n = 11

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

a) At 95% confidence level

= 1 - 95%

=1 - 0.95 =0.05

/2 = 0.025

t/2,df = t_0.025,10 = 2.228

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

= 2.228 * (30.8 / 11)

Margin of error = E = 20.69

The 95% confidence interval estimate of the population mean is,

  ± E

= 166.8  ± 20.69

= ( 146.11, 187.49 )