Question

TEST CORRECTIONS 5. In a study on the benefits of eating organic produce, fruit flies were assigned at random to two groups. One group was fed organic potatoes and the other was fed conventional potatoes. At the end of 13 days, the porportion of flies that were still alive was calculated for each group. To address the question of whether more flies would survive eating organic potatoes than conventional potatoes, we use the hypothesis HO: Porganic = Pconventional vs HA: Porganic > Pconventional

Part A: (got this right)

Part B: Suppose our primary concern is to protect the pubic from potentially harmful pesticides, as found in conventional potatues, and that if no statistically significant difference is found from this test, a grocery chain will stop selling organic potatoes. Is it safer to use a large or small significance level here? Explain in detail.

Part C: The p-value for the data in this study is 0.017. What is the conclusion of the test? State the conclusion in detailed context, using non-technical language.

Part D: A very large sample of fruit flies was used for this study. In the end, 35.8% of the flies eating organic potatoes were still alive, compared to 35.4% of the flies eating conventional potatoes. Comment on the PRACTICAL SIGNIFICANCE of this result. Make a clear distinction between practical and statistical significance.

Answer 1

Part~A: Null Hypothesis H₀: P_organic = P_conventional vs Alternative hypotrhesis H_A: P_organic > P_conventional

where P_organic =true proportion of eating organic potatoes

P_conventional=true proportion of eating conventional potatoes

Part B: It is safer to use use a large significance level.

Small significance level implies rejection region is small and large significance level implies rejection region is large. So if we accept null hypothesis with small significance level there is a possibility to reject null hypothesis with large significance level. Hence it is safer to use a large significance level here.

Part C: The p-value for the data in this study is 0.017. So, 0.01<p-value<0.05. So we reject null hypothesis at 5% level whereas we accept null hypothesis at 1% level. Therefore we conclude that more flies would survive eating organic potatoes than conventional potatoes at 5% level and at 1% level we can't conclude that more flies would survive eating organic potatoes than conventional potatoes.

Part D:

The practically difference between the proportions of eating organic and conventional potatoes= 0.358-0.354=0.004. However suppose we use a sample of size 1000 for both groups then

Test and CI for Two Proportions

Sample X N Sample p
1 358 1000 0.358000
2 354 1000 0.354000

Difference = p (1) - p (2)
Estimate for difference: 0.004
95% lower bound for difference: -0.0312214
Test for difference = 0 (vs > 0): Z = 0.19 P-Value = 0.426

Fisher's exact test: P-Value = 0.444
Here we reject null hypothesis i.e. insignificant difference between the proportions of eating organic and conventional potatoes at 5% level significance (since p-value>0.05)