Discuss the below:
The charitable foundation for a large metropolitan hospital is conducting a study to characterize its donor base. In the past, most donations have come from relatively wealthy individuals; the average annual donor income in the most recent survey was right at $100,000. The foundation believes the average has now increased. A random sample of 200 current donors showed a mean annual income of $103,157 and a standard deviation of $27,498.
To perform this study, we should form a null hypothesis stating that the average is ________ 100,000. (Please fill in only one of the following: "less than", "less than or equal to", "equal to", "greater than", "greater than or equal to". Please do not use symbols.)
At the 10% significant level, the p-value/statistics is ________ so we should ______ the null hypothesis (Please only fill in "reject" or "not reject".).
Hence, we may conclude that the average __________ increased (Please only fill in "has" or "has not") and the probability that our conclusion is correct is ________ percent.