There were 800 math instructors at a mathematics convention. Forty instructors were randomly selected and given an IQ test. The scores produced a mean of 130 with a standard deviation of 10. Find a 95% confidence interval for the mean of the 800 instructors. Use the finite population correction factor.

95% confidence interval for the mean of the 800 instructors is [126.80 , 133.20].

Step-by-step explanation:

We are given that there were 800 math instructors at a mathematics convention.

Forty instructors were randomly selected and given an IQ test. The scores produced a mean of 130 with a standard deviation of 10.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

                           P.Q. =  ~

where, = sample mean score = 130

             s = sample standard deviation = 10

             n = sample of instructors = 40

              = population mean of 800 instructors

Here for constructing 95% confidence interval we have used One-sample t test statistics as we know don't about population standard deviation.

So, 95% confidence interval for the population mean, is ;

P(-2.0225 < < 2.0225) = 0.95  {As the critical value of t at 39 degree of

                                         freedom are -2.0225 & 2.0225 with P = 2.5%}  

P(-2.0225 < < 2.0225) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

95% confidence interval for = [ , ]

                   = [ , ]

                   = [126.80 , 133.20]

Therefore, 95% confidence interval for the mean of the 800 instructors is [126.80 , 133.20].

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