An article contained the following observations on degree of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range: 420 425 427 427 432 433 434 437 439 446 447 448 453 454 465 469
Suppose the sample is from a normal population.
(a) Calculate a 95% confidence interval for the population mean, and interpret it.
(b) Calculate a 95% upper confidence bound for the population mean, and interpret it.

(a) A 95% confidence interval for the population mean is [433.36 , 448.64].

(b) A 95% upper confidence bound for the population mean is 448.64.

Step-by-step explanation:

We are given that article contained the following observations on degrees of polymerization for paper specimens for which viscosity times concentration fell in a certain middle range:

420, 425, 427, 427, 432, 433, 434, 437, 439, 446, 447, 448, 453, 454, 465, 469.

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

                              P.Q.  =    ~

where, = sample mean = = 441

            s = sample standard deviation =  = 14.34

            n = sample size = 16

             = population mean

Here for constructing a 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(-2.131 < < 2.131) = 0.95  {As the critical value of t at 15 degrees of

                                             freedom are -2.131 & 2.131 with P = 2.5%}  

P(-2.131 < < 2.131) = 0.95

P( < < ) = 0.95

P( < < ) = 0.95

95% confidence interval for = [ , ]

                                      = [ , ]

                                      = [433.36 , 448.64]

(a) Therefore, a 95% confidence interval for the population mean is [433.36 , 448.64].

The interpretation of the above interval is that we are 95% confident that the population mean will lie between 433.36 and 448.64.

(b) A 95% upper confidence bound for the population mean is 448.64 which means that we are 95% confident that the population mean will not be more than 448.64.

which expression represents the approximate length of bc?

step-by-step explanation: