Question

A random sample of 9 fields of rye has a mean yield of 35.9 bushels per acre and standard deviation of 2.47 bushels per acre. Determine the 90%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.

Construct the 90% confidence interval. Round your answer to one decimal place.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 35.9

sample standard deviation = s = 2.47

sample size = n = 9

Degrees of freedom = df = n - 1 = 9-1 = 8

At 90% confidence level

= 1-0.90% =1-0.90 =0.10

/2 =0.10/ 2= 0.05

t/2,df = t_{0.05,8 = 1.860}

t _/2,df = 1.860

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

= 1.86 * ( 2.47/ 9)

Margin of error = E =1.531

The 90% confidence interval estimate of the population mean is,

- E < < + E

35.9-1.531 < < 35.9 +1.531

34.4< < 37.4

(34.4,37.4)