The IQ scores of children in a city are assumed to follow anormal distribution with unknown mean μ and known variance σ^2. Arandom sample IQ scores with a size of 25 is drawn by a researcher.Based on this sample, a 97% confidence interval for μ is found tobe (91.49,104.51).
(a) Show that σ=15.
(b) Another random sample of IQ scores with a size of 11 drawnand the scores are recorded as follows:
134, 95,102, 99, 91, 111, 127, 99, 101, 113, 105
Based on the combined information of the two samples, test,atthe 0.05 significance levels, whether or not the mean IQ score ofthe children in the city is less than the national average of105.
