Question

The mean lifetime of a sample of 100 fluorescent light bulbs produced by a company is

Answer 1

Question:

The mean lifetime of a sample of 100 fluorescent light bulbs produced by a  company is computed to be 1570 hr with a standard deviation of 120 hr. If μ is the mean lifetime of all the bulbs produced by a company, test the hypothesis μ = 1600 hr, against the alternative hypothesis μ ≠ 1600 hr, using significance levels of 0.05.

Solution:

Number of fluorescent bulbs, N = 100

Mean lifetime to produce 100 fluorescent bulbs, $\bar{X}$ = 1570

Standard Deviation, σ = 120

μ = 1600 hr

Hypothesis, H₀ = 1600

Alternative Hypothesis, Hₐ ≠ 1600

Significance levels, α = 0.05

The test which we are going to do is a two-sided test for which,

Z-value = ±1.96 which is said to be $Z_{critical} = \pm 1.96$

$\mu_{\bar{X}} = \mu = mean \ of \ sample \ distribution \ of \ standard \ deviation$

$\sigma_{\bar{X}} = \frac{\sigma}{\sqrt{N} } = \frac{\sqrt{120} }{100} = 12.0$

$Test \ statistic, Z = \frac{ \bar{X} - \mu}{\sigma_{\bar{X}} } = \frac{1570 - 1600}{12} = \frac{-30}{12} = -2.50$

$So, Z_{observed} < Z_{critical} \ which \ is \ Z = -2.50 \ lies \ outside \ the \ range \ of \ Z_{critical} \ value$

Therefore, H₀ gets rejected at σ = 0.05

Answer 2

Explanation:

The mean life time of a sample of 100 fluorescent light bulbs

produced by a company is computed to be 1570 hours with a standard deviation

of 120 hours. If is the mean life time of all the bulbs produced by the company,

test the hypothesis hours against the alternative hypothesis

hours, using the level of significance of (a) 0.05 and (b) 0.01.