Question

A random sample of 11 fields of corn has a mean yield of 48.9 bushels per acre and standard deviation of 4.23 bushels per acre. Determine the 95% confidence interval for the true mean yield. Assume the population is approximately normal.

Step 1 of 2:

Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Step 2 of 2:

Construct the 95% confidence interval. Round your answer to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 48.9

sample standard deviation = s = 4.23

sample size = n = 11

Degrees of freedom = df = n - 1 = 11 - 1 = 10

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,10 = 2.228

Margin of error = E = t_/2,df * (s /n)

= 2.228 * (4.23 / 11)

= 2.8

The 95% confidence interval estimate of the population mean is,

- E < < + E

48.9 - 2.8 < < 48.9 + 2.8

46.1 < < 51.7

The 95% confidence interval is (46.1 , 51.7)