A statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77. (SHOW WORK for CREDIT; round to 3 decimal places) a) Estimate the population mean with 93% confidence. b) Repeat Part a) using a 89% level of confidence. c) Repeat Part a) using a population variance equal to 441. d) Repeat Part a) using a sample size equal to 625. Any changes to C. I.?

Step-by-step explanation:

Given that a statistician selected a random sample of 125 observations from a population with a known standard deviation equal to 16 and computed a sample mean equal to 77

We can use Z critical values since population std deviation is known. Also sample size >30

We find std error of mean =

Margin of error = Z critical value * 1.4311

Z critical values for 93% = 1.81

for 89% = 1.60

nStd errorZ critical  Conf interval  

            89%    

1251.4311     1.6  (74.7102479.28976 )

          93%    

            1.81  (74.40970979.590291 )

We find that when confidence level increases interval width increses.

c) When sigma changes to 441, std error changes to

So we get

nStd errorZ critical  Conf interval  

           89%    

441  0.7619     1.6  (75.78178.219 )

         93%    

           1.81  (75.62178.37904)

d) When n = 625, std error changes to 16/25 = 0.64

nStd errorZ critical  Conf interval  

        89%    

4410.641.6        (75.97678.024 )

       93%    

        1.81      (75.84278.1584)

When sample size increases, confidence interval width decreases.