Question

A florist wants to determine if a new additive would help extend the life of cut flowers longer than the original additive. The florist randomly selects 20 carnations and randomly assigns 10 to the new additive and 10 to the original additive. After three weeks, 6 carnations placed in the new additive still looked healthy and 2 carnations placed in the original additive still looked healthy. The difference in proportions (new – original) for the carnations that still looked healthy after three weeks was 0.4. Assuming there is no difference in the additives, 200 simulated differences in sample proportions are displayed in the dotplot.

Using this dotplot and the difference in proportions from the samples, is there convincing evidence that the new additive was more effective?

A. Yes, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
B. Yes, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is statistically significant and the new additive is more effective.
C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.
D. No, because a difference in proportions of 0.4 or less occurred 193 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

Answer 1

Answer: Choice C

C. No, because a difference in proportions of 0.4 or more occurred 7 out of 200 times, meaning the difference is not statistically significant and the new additive is not more effective.

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Step-by-step explanation:

If the new additive was more effective than the old one, then the difference in proportions (new - old) should be fairly large.

Count the dots over the x axis labels of "0.4" through "0.6"

• 5 dots over "0.4"
• 1 dot over "0.5"
• 1 dot over "0.6"

That makes 5+1+1 = 7 dots total.

There are 7 instances where the difference of proportions is 0.4 or larger.

This is out of 200 observations, so 7/200 = 0.035 = 3.5% of the differences have 0.4 or larger.

This is not very significant. The general rule of thumb is to use 5% as the threshold. Some stats textbooks will use 10%. Other times your teacher will specify the significance level. The Greek letter alpha is often used.

Because 3.5% < 5%, we consider the new additive to not be that effective compared to the original additive.