Justin is interested in buying a digital phone. He visited 13 stores at random and recorded...

Justin is interested in buying a digital phone. He visited 13 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of 224.28 and a standard deviation of 20.58.

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

(b) Calculate a 95% confidence interval for the mean price of this model of digital phone

Solutions

Expert Solution

Solution :

Given that,

Point estimate = sample mean = = 224.28

sample standard deviation = s = 20.58

sample size = n = 13

Degrees of freedom = df = n - 1 = 13-1=12

a) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t_/2,df = t_0.025,12 = 2.179

t* = 2.179

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

= 2.179 * (20.58 / $\sqrt$ 13)

= 12.44

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

- E < < + E

224.28 - 12.44 < < 224.28 + 12.44

211.84 < < 236.72

(211.84 , 236.72)

orchestra answered 1 year ago

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