Each of the following is a confidence interval for true ave

Each of the following is a confidence interval for = true average (i.e., population mean) resonance frequency (Hz) for all tennis rackets of a certain type:

(115.4, 116.6) (115.1, 116.9)

a)  The value of the sample mean resonance frequency is ?? .

b) Both intervals were calculated from the same sample data. The confidence level for one of these intervals is 90% and for the other is 99%. Which of the intervals has the 90% confidence level, and why?

            [ Select ]                      

[\"The second interval has the 90% confidence level because it is a narrower interval.\",

\"The first interval has the 90% confidence level because it is a narrower interval.\",

\"The second interval has the 90% confidence level because it is a wider interval.\",

\"The first interval has the 90% confidence level because it is a wider interval.\"]          

Solution

a) mean is 116 because it is the middle of symteric CI

b) first CI is 90% CI because it is narrower, because lower CI level causes lower critical values and narrower CI\'s