EXAMPLE 7.13 More about Wheat Prices
wheat
In the setting of Example 7.12, a quick survey collects prices from only five producers each month. The data are
| Month | Price ($/bushel) | ||||
|---|---|---|---|---|---|
| January | 6.6125 | 6.4775 | 6.3500 | 6.7525 | 6.7625 |
| July | 6.7350 | 6.9000 | 6.6475 | 7.2025 | 7.0550 |
The prices are reported to the nearest quarter of a cent. First, examine the distributions with a back-to-back stemplot after rounding each price to the nearest cent.
386
| January | July | |
| 5 | 6.3 | |
| 8 | 6.4 | |
| 6.5 | ||
| 1 | 6.6 | 5 |
| 65 | 6.7 | 4 |
| 6.8 | ||
| 6.9 | 0 | |
| 7.0 | 6 | |
| 7.1 | ||
| 7.2 | 0 |
The pattern is reasonably clear. Although there is variation among prices within each month, the top three prices are all from July and the three lowest prices are from January.
A significance test can confirm that the difference between months is too large to easily arise just by chance. We test
The price is higher in July . The difference in sample means is 31.7 cents.