Question

QUESTION 2

1. A survey of 100 businesses revealed that the mean after-tax profit was $80,000 and the standard deviation was $15,000.

   Determine the 90% confidence interval estimate of the mean after-tax profit.

   	a.	[76904, 83096]
   	b.	[76130, 83870]
   	c.	[77540, 82460]
   	d.	[78032, 81968]
   	e.	[77060, 82940]

QUESTION 3

1. It is desired to estimate the mean tensile strength for roof hangers.

   It is known that the standard deviation of measurements of tensile strength is 0.25. (Units are Newton per square meter.)

   As it is very important for safety, the 99% confidence interval needs to have a margin smaller than 0.05.

   What is the minimum required sample size?

   	a.	463
   	b.	85
   	c.	167
   	d.	116
   	e.	261

Answer 1

Solution:-

(2). Confidence interval: μ = X0 ± Z_α/2 x (σ / √n)

At 90% confidence level, Z_α/2 = 1.64

μ = 80,000 ± (1.64 x 15,000 / √100)

    = 80,000 ± (1.64 x 15,000 / 10)

    = 80,000 ± 2460

    = 77,540 to 82,460

SO the answer is option (c) 77,540 to 82,460

(3)

Given That,

σ = 0.25

E = 0.05

At 99% confidence level the Z is α = 1 - 99%

                                                                  = 1 - 0.99

                                                                  = 0.01

                                                        α / 2 = 0.005

Z value is = 2.58

Sample Size (n) = (z * σ / E) ^2     

                               = (2.58 * 0.25 / 0.05) ^2

                               = (12.9) ^2

                               = 166.41

SO the answer is Option (C) 167