Question

Q4. [8 marks] The mean μ of the tear strength of a certain paper is under consideration. A sample of size 30 was collected with sample mean 2.4 pounds (a) [4] If the standard deviation of an individual measurement is known to be σ-: 0.2, find a 95% confidence interval for μ. b) l4l if the standard deviation σ is unknown but the sample standard deviation is s-0.2, determine a 95% confidence interval for μ

Answer 1

(a)

n = Sample Size = 30

$\bar{x}$ = Sample Mean = 2.4

$\sigma$ = Population SD = 0.2

SE = $\sigma$/$\sqrt{n}$

= 0.2/ = 0.0365

V30

$\alpha$ = 0.05

From Table, critical values of Z = $\pm$ 1.96

Confidence Interval:

2.4 $\pm$ (1.96 X 0.0365)

= 2.4 $\pm$ 0.0716

=( 2.3284 , 2.4716)

So,

Confidence Interval:

2.3284 < $\mu$ < 2.4716

(b)

n = Sample Size = 30

$\bar{x}$ = Sample Mean = 2.4

s = Sample SD = 0.2

SE = s/$\sqrt{n}$

= 0.2/ = 0.0365

V30

$\alpha$ = 0.05

ndf = 30 - 1 = 29

From Table, critical values of Z = $\pm$ 2.0452

Confidence Interval:

2.4 $\pm$ (2.0452 X 0.0365)

= 2.4 $\pm$ 0.0746

=( 2.3254 , 2.4746)

So,

Confidence Interval:

2.3254 < $\mu$ < 2.4746