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