Question

water dissolved in calcium has no effect on the yields of yellow squash plants. to evaluate this hypothesis, compare the experimental difference of means with the resampling differences. a. collect all the resampling differences of means found in exploration 1(b) for the whole class and display these values in a histogram. b. draw a vertical line on your class histogram to represent the experimental difference of means found in exploration 1(a). c. where on the histogram should the experimental difference of means lie to give evidence for rejecting the hypothesis? d. is your class able to reject the hypothesis? explain your reasoning.

Explanation:

Part (c)

When evaluating a hypothesis using resampling (like a permutation test), the null hypothesis assumes no real difference (the difference is due to random chance). The resampling differences of means represent the distribution of differences we'd expect if the null hypothesis were true. If the experimental difference of means is in the extreme tail(s) of this distribution, it means the observed difference is unlikely to have occurred by chance, providing evidence to reject the null hypothesis.

Part (d)

We compare the experimental difference of means to the distribution of resampling differences (under the null hypothesis). If the experimental difference is rare (in the tail) in this distribution, it suggests the null hypothesis (no effect) is unlikely, so we reject it. If it's common (in the middle), the null hypothesis is plausible, so we fail to reject it. The specific decision relies on where the experimental difference falls relative to the resampling distribution from the class data.

Answer:

The experimental difference of means should lie in the tail(s) of the histogram (either far to the left or far to the right) of the resampling differences of means to give evidence for rejecting the hypothesis.