Question

MORE BENEFITS OF EATING ORGANIC

Using data from a study, we find a significant difference in the proportion of fruit 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 additional data from this study.¹ In this case, we are testing

H0:po=pcHa:po>pc

where po and pc represent the proportion of fruit flies alive at the end of the given time frame of those eating organic food and those eating conventional food, respectively. We have n1=n2=500. Show all remaining details in the test, using a 5% significance level.

Effect of Organic Bananas After 15 Days

After 15 days, 345 of the 500 fruit flies eating organic bananas are still alive, while 320 of the 500 eating conventional bananas are still alive.


¹Proportions approximated from information given in the paper.

Give the test statistic and the p-value.

Round your answers to three decimal places.

Test statistic = __________________.

p-value = ______________________.

What is the conclusion?
Reject H_0. OR Do not reject H_0.???

Do we have evidence that the proportion surviving after eating organic is higher?

Yes or No?

Answer 1

For Organic:

n1 = 500, x1 = 345

p̂1 = x1/n1 = 0.69

For conventional :

n2 = 500, x2 = 320

p̂2 = x2/n2 = 0.64

α = 0.05

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 > p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (345+320)/(500+500) = 0.6650

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.69 - 0.64)/√[0.665*0.335*(1/500+1/500)] = 1.675

p-value = 1- NORM.S.DIST(1.675, 1) = 0.047

Decision:

As p-value < α, reject the null hypothesis.

Conclusion:

Yes, There is enough evidence to conclude that the proportion surviving after eating organic is higher