STATS List below are the ages (years) of randomly selected race car drivers. Construct a 95% confidence interval estimate of the mean age of all race car drivers: ages 32, 40, 27, 36, 29, 28

A 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].

Step-by-step explanation:

We are given below the ages (in years) of randomly selected race car drivers;

Ages: 32, 40, 27, 36, 29, 28.

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

                           P.Q.  =    ~

where, = sample mean age = = = 32 years

           s = sample standard deviation =  = 5.1 years

           n = sample of car drivers = 6

            = population mean age of all race car drivers

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

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

P(-2.571 < < 2.571) = 0.95  {As the critical value of t at 5 degrees of

                                                freedom are -2.571 & 2.571 with P = 2.5%}  

P(-2.571 < < 2.571) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

95% confidence interval for = [ , ]

                                                  = [ , ]

                                                  = [26.65, 37.35]

Therefore, a 95% confidence interval estimate of the mean age of all race car drivers is [26.65 years, 37.35 years].

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step-by-step explanation:

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