A random sample of 8 fields of barley has a mean yield of 49.6 bushels per acre and standard deviation of 2.33 bushels per acre. Determine the 99% confidence interval for the true mean yield. Assume the population is approximately normal. Step 1 of 2 : Find the critical value that should be used in constructing the confidence interval. Round your answer to three decimal places.

99% confidence interval for the true mean yield is [46.718 , 52.482].

Step-by-step explanation:

We are given that a random sample of 8 fields of barley has a mean yield of 49.6 bushels per acre and standard deviation of 2.33 bushels per acre.

Firstly, the pivotal quantity for 99% confidence interval for the true mean yield is given by;

         P.Q. = ~

where, = sample mean yield = 49.6 bushels per acre

             s = sample standard deviation = 2.33 bushels per acre

             n = sample of fields of barley = 8

              = true population mean

Here for constructing 99% confidence interval we have used t statistics because we don't know about population standard deviation.

So, 99% confidence interval for the true mean, is ;

P(-3.499 < < 3.499) = 0.99  {As the critical value of t at 7 degree of

                                                freedom are -3.499 & 3.499 with P = 0.5%}

P(-3.499 < < 3.499) = 0.99

P( < < ) = 0.99

P( < < ) = 0.99

99% confidence interval for = [ ,  ]

                                                 = [ , ]

                                                 = [46.718 , 52.482]

Therefore, 99% confidence interval for the true mean yield is  [46.718 , 52.482].

fist on the left goes with the third on the right. second on the left goes with the fourth on the right. third on the left goes with the second on the right. the fourth on the left goes with first on the right

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6