QUESTION: In Illinois a random sample of 85 eight grade students has a mean score of 265 on a national math assessment test. Based on historical date, the population standard deviation is estimated to be 55. Based on the sample mean of 265, a state administrator declares that the mean score for the eighth graders in state of Illinois on the national math assessment examination is more than 260. At alpha = 0.04, is there enough evidence to support the administrator's claim?
I would like each student to answer one part of the following 5-part question. The next student checks ALL the answers to the previous parts for correctness. If any of them is wrong, the student will correct it and explains in detail to his/her classmates why it was wrong. If answers to all previous parts are correct, the student shall answer the next unanswered part or build on one of the previously posted correct responses. Here are the 5 parts.
- Write Ho and Ha mathematically and identify the claim. Then, explain why you set up your hypotheses the way did in enough detail that your classmates who could not do this part correctly can follow and understand your reasoning
- Find the standardized test statistic z and its corresponding area under the distribution curve. Explain how you did it.
- Find the p-value. Show and explain your work in detail so your classmates who could not do this part can understand and follow your approach
- Decide whether to reject Ho or not. Explain your logic in detail
- Fully interpret the decision in the context of the original claim