Question

An egg farmer wanted to determine if increasing the length of time the lights were on in his hen house would increase egg production. For a sample of eight chickens he determined their production before and after increasing the amount of time the lights were on. The sample mean of the paired differences yields a sample mean of 2 and a sample standard deviation of 1.5119. At the 0.01 significance level, has there been an increase in production?

Conduct the appropriate hypothesis test and report the p-value. Do not round intermediate calculations. Round your answer to four decimal places. Include the leading zero. Format: 0.0000

Answer 1

Null and alternative hypotheses

Ho : D = 0

H1 : D > 0

Level of significance a = 0.01

Test statistic t

t = dbar /( sd /√n) = 2/(1.5119/√8)

t = 3.74

tCritical for a = 0.01 and d.f = n -1 = 7

tCritical = t​​​​​​0.99 , 7

tCritical = 3.00

Here t = 3.74 > tCritical = 3.00

Conclusion : Reject the null hypothesis Ho , sufficient evidence to conclude that  there been an increase in egg production after increasing the length of time the lights

p-value = P ( t > 3.74) d.f = 7

p-value = 0.0036