Wiki Page, Math 13 - Perez Sandbox : ANSWER(S): Module 24 - Matched Pairs Lab (4d of 5 discussion 2)

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2026-01-17T21:14:50-08:00

1. State hypotheses:
Define as the mean of the differences "regular − kiln-dried" in the corn yield for a plot of land. Since we want to test the hypothesis that kiln-dried seed yields more corn than regular seed, a negative difference supports this hypothesis; therefore, the alternative hypothesis is "mean of the differences is less than zero."
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(Note: if the difference was defined in the reverse order kiln-dried − regular, then the alternative hypothesis would be . Either definition of the difference is fine, but the alternative hypothesis has to be consistent with whichever definition you choose.)

2. Check conditions:

1. The variable is "difference in yield," which we defined as kiln-dried − regular, so we analyze the dotplot of differences.

2. The sample size is quite small (n = 11), so it is difficult to determine if the shape of the distribution. However, we can see that the data (differences) are not heavily skewed and there are no extreme outliers; therefore, we assume that the distribution of differences in yield for all seeds will be normal and we proceed with the T-test.

3. Even though the problem does not state it specifically, we can assume that Gosset knew what he was doing and he choose the seeds at random. The use of matched-pairs design controls for idiosyncratic differences in the plots, e.g. one plot being more fertile or getting more sun, etc.

3. Here are the StatCrunch results.

Paired T hypothesis test:
: Mean of the difference between Regular seed and Kiln-dried seed
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Hypothesis test results

Difference | Mean | Std. Err. | DF | T-Stat | P-value
Regular seed - Kiln-dried seed | -33.727273 | 19.951346 | 10 | -1.6904761 | 0.0609

Differences stored in column, Differences.

The test statistic is –1.69 and the P-value is 0.061. Even though the P-value is quite small, it is not small enough if we use a significance level of 0.05. This means that even though the data show some evidence against the null hypothesis, it isn't quite strong enough to reject it.

4. Conclusion: The data from this experiment do not provide strong enough evidence to conclude that kiln-dried seeds yield more corn than regular seeds.