A survey of the age of people denied promotion was conducted. In a random sample of 23 people the average age was 47.0 with a sample standard deviation of 7.2 Assume this sample comes from a population that is normally distributed. a. Calculate the EBM then construct a 95% confidence interval for the average of the age of people denied (round the values of the interval to 1 decimal place). b. If a manager claimed that the average age of people denied promotion was 51, would you agree or disagree based on your confidence interval? Explain your reasoning.

(a) 95% confidence interval for the average of the age of people denied is [43.9 , 50.1].

(b) Based on our confidence interval, we would disagree with the manager's claim.

Step-by-step explanation:

We are given that a survey of the age of people denied promotion was conducted. In a random sample of 23 people the average age was 47.0 with a sample standard deviation of 7.2.

Assume this sample comes from a population that is normally distributed.

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

                            P.Q. =    ~

where, = sample average age = 47.0

            = sample standard deviation = 7.2

            n = sample of people = 23

             = true average of the age of people denied

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

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

P(-2.074 < < 2.074) = 0.95  {As the critical value of t at 22 degree

                                       of freedom are -2.074 & 2.074 with P = 2.5%}  

P(-2.074 < < 2.074) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

(a) 95% confidence interval for = [ , ]

                                           = [ , ]

                                           = [43.9 , 50.1]

Therefore, 95% confidence interval for the average of the age of people denied is [43.9 , 50.1].

(b) Based on our confidence interval, we would disagree with the manager's claim that the average age of people denied promotion was 51 because the interval doesn't contain the value 51.