Question

2. Many people pay more to eat organic when possible, but does eating organic food actually

offer health benefits? Spurred on by her parents debating this question, a 16-year old girl decided

to investigate it with a science project. She randomly divided fruit flies into two groups and fed

one group conventional potatoes and the other group organic potatoes. She examined the survival

of fruit flies. After 11 days 68% of the fruit flies eating organic potatoes are still alive while 66%

of the fruit flies eating conventional potatoes are still alive. The standard error for the difference

in proportion is 0.030. Test at 5% significance level whether eating organic potatoes improves

survival of fruit flies. Assume the samples is sufficiently large enough to use normal curve.

Define the parameters and give the notation and value of the observed sample statistic. Show all

steps of the test.

Answer 1

proportion of living fruit flies eating organic potatoes= 0.68

proportion of living fruit flies eating conventional potatoe = 0.66

difference in sample proportions, p̂1 - p̂2 =     0.6800   -   0.6600   =   0.0200

standard error for the difference in proportion = 0.03

Z-statistic = (p̂1 - p̂2)/SE = (   0.020   /   0.0300   ) =   0.6667

p-value =    0.2525   [excel function =NORMSDIST(-z)]

decision :    p-value>α,Don't reject null hypothesis

so , eating organic food does not actually offer health benefits

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