Question

a. The average IQ is 100, with a population standard deviation of 15. The mayor of Smartsville claims that citizens in his town have higher than average IQs. To test that claim, 40 Smartsville citizens were randomly selected, and their average IQ was determined to be 104.1. Does this support the mayor’s claim? Use ? = 0.1. b. construct a 90 % confidence interval for the mean. Does the confidence interval support the claim made in part a? Preferably, solve using MegaStat.

Answer 1

a ) To test :

Test statistic :

where ,

We reject the null hypothesis or H₀ if the observed value of of , where ,

The value of the test statistic :  

Critical value :  

Now ,

Hence we reject the null hypothesis or H₀ .

Thus we have sufficient evidence to support the mayor's claim .

b ) The 90 % confidence interval of the population mean is :

where ,

Required confidence interval :  

Hence the confidence interval support the claim made in part a