Question

(1 point) A random sample of n measurements was selected from a population with unknown mean u and standard deviation o. Calculate a 90% confidence interval for p for each of the following situations: (a) n = 100 = 102.2, s = 2.28 << (b) n=90, Z = 84.8, s = 2.19 <u (c) n = 80, Z = 55.8, s 2.48 << (d) n=90, = 76.3, s = 2.68 Sus Note: You can earn partial credit on this problem.

Answer 1

Answer:

Given,

Here at 90% CI, z value is 1.645

a)

sample n = 100, xbar = 102.2 , s = 2.28

90% CI = xbar +/- z*s/sqrt(n)

substitute values

= 102.2 +/- 1.645*2.28/sqrt(100)

= 102.2 +/- 0.3751

= (101.825 , 102.575)

b)

sample n = 90, xbar = 84.8, s = 2.19

90% CI = xbar +/- z*s/sqrt(n)

substitute values

= 184.8 +/- 1.645*2.19/sqrt(90)

= 184.8 +/- 0.3797

= (184.420 , 185.180)

c)

sample n = 80, xbar = 55.8, s = 2.48

90% CI = xbar +/- z*s/sqrt(n)

substitute values

= 55.8 +/- 1.645*2.48/sqrt(80)

= 55.8 +/- 0.456

= (55.344 , 56.256)

d)

sample n = 90, xbar = 76.3, s = 2.68

90% CI = xbar +/- z*s/sqrt(n)

substitute values

= 76.3 +/- 1.645*2.68/sqrt(90)

= 76.3 +/- 0.465

= (75.835 , 76.765)