Question

For the following data values below, construct a 90% confidence interval if the sample mean is known to be 0.719 and the population standard deviation is 0.366. (Round to the nearest thousandth) (Type your answer in using parentheses!Use a comma when inputing your answers! Do not type any unnecessary spaces! List your answers in ascending order!) for example: (0.45,0.78)

0.56, 0.75, 0.10, 0.95, 1.25, 0.54, 0.88

Answer 1

SOLUTION:

From given data,

For the following data values below, construct a 90% confidence interval if the sample mean is known to be 0.719 and the population standard deviation is 0.366. (Round to the nearest thousandth) (Type your answer in using parentheses!Use a comma when inputing your answers! Do not type any unnecessary spaces! List your answers in ascending order!) for example: (0.45,0.78)

0.56, 0.75, 0.10, 0.95, 1.25, 0.54, 0.88

We have,

Sample Mean = = 0.719

Population Standard deviation = = 0.366

Sample size = n = 7

90% confidence interval

Confidence interval is 90%

90% = 90/100 = 0.90

= 1 - Confidence interval = 1-0.90 = 0.10

/2 = 0.10 / 2

= 0.05

Z_/2 = Z_0.05 = 1.64

for the population mean µ

   Z_/2 ( / )

   Z_0.05 ( / )

0.719 1.64 (0.366 / )

0.719 1.64 (0.366 /2.645751)

0.719 1.64 0.138335

0.719 0.2268694

(0.719-0.2268694,0.719+0.2268694)

(0.4921306,0.9458694)

(0.49,0.95)