The U.S. Department of Agriculture (USDA) uses sample surveys to produce important economic estimates. One pilot study estimated durum wheat prices in July and in January using independent samples of wheat producers in the two months.
The data is given in Excel under the WHEAT PRICES sheet.
Although there is variation among prices within each month, the top four prices are all from July and the four lowest prices are from January. You will run a significance test to check if the difference between months is just by chance. You'll use $\alpha = 0.05$ for significance test. Assume that the two Normal population distributions have the same standard deviation.
a. Write out the null and alternative hypothesis associated with the research question. (2p)
b. What type of statistical test will you use to answer the proposed research question? (Note: Is this a z-test or a t-test? (2p)
c. What is the critical value at the 0.05 level of significance? Be sure and include whether this critical value is a z or t value and, if appropriate, include the degrees of freedom associated with this statistical test. (4p)
d. What is the calculated value of the test statistic? (4p)
e. What decision should be made about the null hypothesis? In other words, should you reject or retain the null hypothesis? (3p)
