According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is 54

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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According to a report done by S & J Power, the mean lifetime of the light bulbs it manufactures is
54
months. A researcher for a consumer advocate group tests this by selecting
50
bulbs at random. For the bulbs in the sample, the mean lifetime is
53
months. It is known that the population standard deviation of the lifetimes is
8
months. Can we conclude, at the
0.10
level of significance, that the population mean lifetime,
μ
, of light bulbs made by this manufacturer differs from
54
months?

Perform a two-tailed test. Then complete the parts below.

Carry your intermediate computations to three or more decimal places, and round your responses as specified below. (If necessary, consult a list of formulas.)

(a) State the null hypothesis
H0
and the alternative hypothesis
H1
.
H0:
H1:
(b) Determine the type of test statistic to use.
  ▼(Choose one)
 
(c) Find the value of the test statistic. (Round to three or more decimal places.)
 
(d) Find the two critical values. (Round to three or more decimal places.)
and
(e) Can we conclude that the population mean lifetime of light bulbs made by this manufacturer differs from
54
months?
 
Yes
 
No
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