Question

An agricultural researcher is interested in estimating the mean length of the growing season in a region. Treating the last 10 years as a simple random sample, he obtains the following data, which represent the number of days of the growing season.
153 164 147 141 172 183 195 178 163 151

A) Construct a 95% confidence interval for the mean lenght of the growing season in the region. _______
(use asending order. round to two decimal places as needed)

Answer 1

Here the population variance is not known, so use student-t distribution.

A 95% (two-tail) confidence interval would include the limits.
The value 1.96 comes from a T-value for 97.5% (half tail).

x&#0772-Ts ≤ μ ≤ x&#0772+Ts

where x̄=sample mean
s=sample variance.
T=value from student-t distribution for 97.5% and ν=n-1=9 (degrees of freedom)