Question

Suppose a sample of 21 is drawn from a population that has a continuous random variable x that is well-approximated by a normal distribution. If the sample mean is given by ?̅= 202.4 with standard deviation s = 26 find

a) a 98% Confidence interval for ?. Be sure to include pictures and graphs that would support your work.

b) State specifically how you would interpret this interval.

Answer 1

n = 21

S = 26

x̅ = 202.4

Standard Error = S / √n

                                   = 26 / √21

                                   = 5.6736

               Standard Error = 5.6736

Confidence Interval = Mean + - Margin Error

Confidence Interval = Mean + - ( Critical value* Standard Error)

For Critical value:

               ꭤ = 1 – 0.98 = 0.02

P value = 1 – (ꭤ/ 2)

              = 1 – (0.02/2)

              = 1 – 0.01

              = 0.99

From Z table we get

Critical value = 2.33

Now,

Confidence Interval = Mean + - ( Critical value* Standard Error)

                                   = 202.4 + - ( 2.33 * 5.6736)

                                   = 202.4 + - 13.2194

= 189.1806 and 215.6194

Confidence Interval = 189.1806 and 215.6194