MORE DCNEFITS OF EATING ORGANIC

Using data from a study, we find a significant difference in the proportion of frult flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using addittonat ditis from this study. in this case, we are testing

where and represent the proportion of fruit flies allive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have . Show all remaining details in the test, using a significance level.

Effect of Organic Raisins After 20 Days
After 20 days, 275 of the 500 fruit fles eating organic raisins are still alive, while 170 of the 500 eating comventional ralsins are still alive.
Proportions approximated from information given in the paper.

Part 1
(7) Your answer is partlaily correct.

Give the test statistic and the p-value.
Round your answers to three decimal places.

Test statistic

Ask by Ford Christensen. in the United States

Mar 28,2025

Question

MORE DCNEFITS OF EATING ORGANIC

Using data from a study, we find a significant difference in the proportion of frult flies surviving after 13 days between those eating organic potatoes and those eating conventional (not organic) potatoes. This exercise asks you to conduct a hypothesis test using addittonat ditis from this study. in this case, we are testing

where and represent the proportion of fruit flies allive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have . Show all remaining details in the test, using a significance level.

Effect of Organic Raisins After 20 Days
After 20 days, 275 of the 500 fruit fles eating organic raisins are still alive, while 170 of the 500 eating comventional ralsins are still alive.
Proportions approximated from information given in the paper.

Part 1
(7) Your answer is partlaily correct.

Give the test statistic and the p-value.
Round your answers to three decimal places.

Test statistic

Ask by Ford Christensen. in the United States

Mar 28,2025

UpStudy AI · Accepted Answer

The pooled proportion is calculated as

$$
\hat{p}=\frac{275+170}{500+500}=\frac{445}{1000}=0.445.
$$

Then, the test statistic is given by

$$
Z=\frac{\hat{p}_{o}-\hat{p}_{c}}{\sqrt{\hat{p}(1-\hat{p})\left(\frac{1}{n_{o}}+\frac{1}{n_{c}}\right)}},
$$

where

$$
\hat{p}_{o}=\frac{275}{500}=0.55\quad\text{and}\quad \hat{p}_{c}=\frac{170}{500}=0.34.
$$

Substituting the values, we have

$$
Z=\frac{0.55-0.34}{\sqrt{0.445\cdot(1-0.445)\left(\frac{1}{500}+\frac{1}{500}\right)}}=\frac{0.21}{\sqrt{0.445\cdot0.555\cdot\frac{2}{500}}}.
$$

First, calculate the product in the denominator:

$$
0.445\cdot0.555\approx0.247\quad \text{and}\quad \frac{2}{500}=0.004.
$$

So,

$$
\sqrt{0.247\cdot0.004}\approx\sqrt{0.000988}\approx0.031.
$$

Thus, the test statistic is

$$
Z\approx\frac{0.21}{0.031}\approx6.778.
$$

(Rounding to three decimal places, one might obtain $$6.778$$ or a value very close depending on intermediate rounding; here we use $$6.778$$.)

The p-value for a right-tailed test is

$$
\text{p-value}=1-\Phi(Z).
$$

Given that a $$Z$$ of approximately $$6.778$$ is extremely high, the p-value is effectively

$$
\text{p-value}\approx0.000.
$$

Thus, the answers are:

Test statistic $$=6.778$$ and p-value $$\approx 0.000$$.
Test statistic $$=6.778$$ and p-value $$\approx 0.000$$.