Question

Problem2:

The high temperatures (in degrees Fahrenheit) of a random sample of 6 small towns are:

98.7

98.5

98.2

99.2

98

98.9

Assume high temperatures are normally distributed. Based on this data, find the 90% confidence interval of the mean high temperature of towns. Enter your answer as an open-interval (i.e., parentheses) accurate to two decimal places (because the sample data are reported accurate to one decimal place).

90% C.I. =

Answer should be obtained without any preliminary rounding. However, the critical value may be rounded to 3 decimal places.

Answer 1

sample mean, xbar = 98.58
sample standard deviation, s = 0.4446
sample size, n = 6
degrees of freedom, df = n - 1 = 5

Given CI level is 90%, hence α = 1 - 0.9 = 0.1
α/2 = 0.1/2 = 0.05, tc = t(α/2, df) = 2.015

CI = (xbar - tc * s/sqrt(n) , xbar + tc * s/sqrt(n))
CI = (98.58 - 2.015 * 0.4446/sqrt(6) , 98.58 + 2.015 * 0.4446/sqrt(6))
CI = (98.21 , 98.95)