You are told that the population of the scores of IQ test takers is normally distributed, has a population mean of 100 and a standard deviation of 10. You get a sample of 100 takers and find out that the mean score of those takers is 101.9.
a) At a 0.10 significance level, do you have enough evidence, based on the sample, to conclude that this mean score may have changed?
b) At a 0.05 significance level, do you have enough evidence, based on the sample, to conclude that this mean score may have changed?
c) At a 0.01 significance level, do you have enough evidence, based on the sample, to conclude that this mean score may have changed?
d) What is the maximum level of significance required that would make you conclude that the mean score has changed?