Question

A random sample of 27

fields of rye has a mean yield of 45.4
bushels per acre and standard deviation of 3.17
bushels per acre. Determine the 99%
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 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

Answer 1

The critical value for a 99% confidence interval is 2.779.

How to determine critical value of a random sample.

For a 99% confidence interval

Degrees of freedom = n - 1 = 27 - 1 = 26

For 26 df and 99% confidence interval,

Critical value = 2.779

Since it's a two-tailed test (upper and lower confidence bounds), allocate 0.5% to each tail. The remaining 99% is in the middle.

The critical value for a 99% confidence interval is often denoted as Zα/2, where α is the significance level, and α/2 is the tail probability.

Z α = Z(0.005)

using a standard normal distribution table.

The critical value Z for a cumulative probability of 0.005 is approximately 2.779.

Therefore, the critical value for a 99% confidence interval is 2.779.