Question

Peele is interested in the average price of an entree at a French restaurant, but only has a random sample of 9 prices (prices are not listed on the menu). Using this random sample, Key calculates that a 90% confidence interval for the true mean is given by (65, 88). (You can assume the prices follow a normal distribution). Use this information to do the following:

a) Calculate 7. (Hint, what does a confidence interval look like?)
b) Calculate s.
c) Construct a 95% confidence interval for the true mean price of all the entrees, f.

Answer 1

Xbar = 76.5

s = 24.70

(61.19 ; 91.81)

Explanation:

Given that :

Confidence interval = (65, 88)

Recall:

Confidence interval = xbar ± margin of error

Margin of Error = (upper boundary - lower boundary) / 2

Margin of Error = (88 - 65) /2 = 11.5

Taking the lower boundary :

Lower boundary = xbar - margin of error

xbar = lower boundary + margin of error

Xbar = 65 + 11.5

Xbar = 76.5

Margin of Error = Tcritical * s/sqrt(n)

s = sample standard deviation

Tcritical at 90% confidence, df = 9-1= 8 = 1.397

11.5 = 1.397 * s/sqrt(9)

11.5 = 1.397 * s/3

34.5 = 1.397s

s = 34.5 / 1.397

s = 24.695

s = 24.70

C.) 95% confidence interval :

Tcritical at 95%, df = 8 = 1.860

Margin of Error = 1.860 * 24.70/sqrt(9) = 15.311

Confidence interval :

Lower boundary = 76.5 - 15.311

Upper boundary = 76.5 + 15.311

(61.19 ; 91.81)