Question

The production of pasture grass for hay is an important agricultural product. A new type of grass, called Teff Grass is advertised to produce 2 ton of hay per acre on the first cutting. Twenty-five test plots of this new grass resulted in average production of 1.92 ton per acre on the first cutting with a standard deviation of 0.40 ton. Assume that the production of hay is a normally distributed random variable, which is a necessary assumption with this small sample.

1. What is the 99% confidence interval to estimate the parameter based on these data?
2. Does the above confidence interval contain the hypothesized parameter value in this case? Write a sentence about what the confidence interval indicates about the parameter value.

Answer 1

Solution:

Given:

Sample size = n = 25

Sample mean =

Sample standard deviation = s= 0.40

Population mean =

Part a)

We have to find the 99% confidence interval to estimate the parameter based on these data

Formula:

where

t_c is t critical value for c = 99%  confidence level

Thus two tail area = 1 - c = 1 - 0.99 = 0.01

df = n - 1 =  25 - 1 = 24

t_c = 2.797

Thus

Thus

Part b)

This 99% confidence interval includes the population mean value of 2 ton.

thus this  confidence interval indicates that the the population mean value is equal to 2 ton.

Thus  a new type of grass, called Teff Grass is advertised to produce 2 ton of hay per acre on the first cutting is true.