Question

The life span of 100 W light bulbs manufactured by a particular company follows a normal distribution with a standard deviation of 120 hours, and its average life time is guaranteed for a minimum of 800 hours. A delivery of 10,000 of light bulbs is sent to a wholesale store, and the quality control staff in the store randomly selected 50 bulbs to test the life time. The average life time of the sample is found out to be 760 hours, with a standard deviation of 145 hours.

1. The bulbs should have at least 800 hours of average life time, as promised by the manufacturer. When the bulb is delivered to the store, the store manager will need to evaluate on the quality, and his concern will be the average life time of all 10,000 light bulbs is less than 800 hours. Perform a hypothesis test to address his concern at 0.02 significance level.

1. State your hypothesis.

Ho: μ _____ (μ is average life time of all 10,000 bulbs of the delivery).

Ha: μ _____

2. Rejection rule: If p < ______, then reject Ho.

3. Test statistic calculation: Z = _____________.

By looking at your alternative hypothesis, determine p-value for this test.

p-value = _____________.

4. Apply rejection rule, since p ____ 0.02, ________ Ho.

5. Conclusion:

f. Based on your inference above, what type of error could you possibly make (Type I error or type II error)?

Answer 1

Given

$\mu$ = 800 hr

$\sigma$ = 120

= 760

T

n = 50

(a) Null and alternative hypothesis

Ho: μ $\geq$ 800

Ha: μ < 800

(b) Rejection rule: If p < 0.02 then reject Ho.

(c) Test statistic calculation:

I N - g/n

$Z=\frac{760-800 }{120 /\sqrt{50}}$

$Z=\frac{760-800 }{120 /\sqrt{50}} =\frac{-40}{16.97056275} =-2.3570$

p-value = 0.0092

Rejection rule

(d) p-value (0.0092) < 0.02

Reject H0

(e)Conclusion: We conclude that Average life time of bulbs is less than 800 hours

(f) Type I error