Question: A researcher claims that the intelligence of children in a particular community is above average. To test this claim, the researcher selects a simple random sample consisting of 9 children from the population. Scores of the intelligent test typically vary according to a Normal Distribution with a mean ( \(\mu \) ) of 100 and population standard deviation ( \(\sigma \) ) of 15. The sample of the 9 children produced the following scores: 116, 128, 125, 119, 89, 99, 105, 116, and 118. Does this sample provide statistical significant evidence in support of the researcher's claim?

Show all you work and including your hypotheses, test statistic, p-value, and your conclusion. Choose your significant level for your test when you state your conclusion.