An egg farmer wanted to determine if increasing the amount of time the lights were on in his hand house would increase egg production. For example of 8 chickens he determined the production before and after increasing the amount of time the lights were on. The sample mean for before was 5.125 and the sample mean after is 6.75. The sample standard deviation of the difference is 3.962. Add the 5% significance level, has there been an increase in production? What is alternative hypothesis and p-value?