Question

(1 point) Justin is interested in buying a digital phone. He visited 17 stores at random and recorded the price of the particular phone he wants. The sample of prices had a mean of $217.47 and a standard deviation of $20.75. (a) What critical value t* should be used for a 95% confidence interval for the mean, u, of the distribution? ** (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.) $ to $ Note: Round your answer to 2 decimal places.

Answer 1

a) n = 17 ==> df = n-1 = 16

95% CI ==> $\alpha$ = 0.05

critical value, t* = 2.120 (from t-table)

b) $CI: \bar{x} \pm t* \times \displaystyle\frac{s}{\sqrt{n}}$

$= 217.47 \pm 2.120 \times \displaystyle\frac{20.75}{\sqrt{17}}$

= ( 206.80, 228.14)

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