Question

Has the mean price of corn changed over the past year? The mean price of corn sold in April 2017 was $2.00 per bushel. A sample of 22 transactions for the sale of corn in April 2018 has a mean $2.08 and standard deviation $0.20. The price for such transactions is known to be normally-distributed. Test using 5% significance.

Define the population parameter. (a) µ = mean price of corn in April 2017 (b) µ = mean price of corn in April 2018 (c) t = mean price of corn in April 2018 (d) Z = mean price of corn in April 2017 (e) x = price for an individual corn transaction in April 2018

Answer 1

Given the sample size and sample mean , sample standard deviation .

Here . Since the population standard deviation is not known, we use t-distribution.

Degrees of freedom is .

The hypotheses are

The test statistic is

The p-value is

Since the , we accept the null hypothesis. The conclusion is

The mean price of corn has not changed over the past year.

The population parameter is (b) µ = mean price of corn in April 2018. (since we are making a claim about the prices in 2018).