Question

A manufacturer of new light bulbs claims the average lifetime of its long-life bulb is more than 4000 hours. To test this claim, a reputable testing firm took a random sample of 100 bulbs and life tested them. The testing firm found the average life of the sample to be 4500 hours with a sample standard deviation, s = 400 hours. The value of the test statistic for this problem isA 1.25B -1.25C 12.5D -12.5E None of the values listed

Answer 1

Answer: C. 12.5

Explanation:

Given : A manufacturer of new light bulbs claims the average lifetime of its long-life bulb is more than 4000 hours.

Population mean :
`\mu=4000`

Sample size : n= 100

Sample mean :
`\overline[x}=4500`

Standard deviation:
`s=400`

The value of test-statistic is given by :-

`z=\frac{\overline{x}-\mu}{(s)/(√(n))}\\\\\Rightarrow\ z=(4500-4000)/((400)/(√(100)))\\\\\Rightarrow\ z= 12.5`

Hence, the value of the test statistic for this problem is 12.5.