In: Statistics and Probability
a) A researcher is interested in determining if the IQ’s of prison inmates differs from the that the general population, which has been shown to have a mean IQ of 100 and a standard deviation of 15. The researcher recruits a random sample of 25 inmates and finds that the average IQ is 105.3 points. Test the null hypothesis at the .05 level. Show all work and present a step by step hypothesis test summary as shown in the text.
b) Find the 99% confidence interval for the data above and explain what the confidence interval tell us about the true mean of the population for this sample.