investigators at an agricultural research facility randomly assigned equal numbers of chicken to be housed in two rooms. In room #1, chickens experienced normal day/night cycles. In the other room, lights were left on 24 hours a day. The objective was to see which group of chickens would lay more eggs. After collecting data for several days, the researchers tested the hypothesis against the one-tail alternative and found p-value = 0.22. Which of the following statements is true ?
A) The chickens in the lighted room averaged 0.22 more eggs per day
B) Theres a 22% chance that chickens house in a lighted room produce more eggs.
C) Theres a 22% chance that theres really no difference in egg production.
D) Theres a 22% chance another experiment will give these same results.
E) None of theses.
E. with a P-Value greater than 5%, you fail to reject the null hypothesis. Therefore there is no difference.
The correct statement is:
C) There's a 22% chance that there's really no difference in egg production.
Explanation:
The p-value is used to determine the level of evidence against the null hypothesis. In this case, the null hypothesis would be that there is no difference in egg production between the two groups of chickens (normal day/night cycle chickens vs. chickens with lights on 24 hours).
A p-value of 0.22 indicates that there is a 22% chance of observing the data (or more extreme data) given that the null hypothesis is true. Therefore, it suggests that there is not enough evidence to reject the null hypothesis and conclude that there is a difference in egg production between the two groups of chickens.
To determine which statement is true, let's analyze the given options and understand their meanings:
A) The statement says that "The chickens in the lighted room averaged 0.22 more eggs per day." However, the p-value of 0.22 does not directly tell us the difference in egg production between the two groups. The p-value indicates the strength of evidence against the null hypothesis, but it does not provide information about the magnitude of the difference. Therefore, option A is not true.
B) This statement claims that "There's a 22% chance that chickens housed in a lighted room produce more eggs." The p-value of 0.22 does not represent the probability or chance that the lighted room group produces more eggs. The p-value is the probability of observing the data (or more extreme) under the assumption that the null hypothesis is true. So option B is not true.
C) This statement states that "There's a 22% chance that there's really no difference in egg production." The p-value of 0.22 indicates that there is not enough evidence to reject the null hypothesis, which assumes no difference in egg production between the groups. So option C correctly describes the interpretation of the p-value in this scenario.
D) This statement states that "There's a 22% chance another experiment will give these same results." The p-value does not provide any information about the likelihood of obtaining the same results in a future experiment. The p-value represents the probability of observing the current data or more extreme if the null hypothesis is true. It does not relate to the likelihood of replication. Therefore, option D is not true.
Based on the analysis, the correct answer is C) There's a 22% chance that there's really no difference in egg production.