A company manufactures light bulbs. The company wants the bulbs to have a mean life span of 999 hours. This average is maintained by periodically testing random samples of 25 light bulbs. If the t-value falls between minus−t 0.95 and t 0.95 then the company will be satisfied that it is manufacturing acceptable light bulbs. For a random sample, the mean life span of the sample is 1006 hours and the standard deviation is 22 hours. Assume that life spans are approximately normally distributed. Is the company making acceptable light bulbs? Explain.
The company is or is not making acceptable light bulbs because the t-value for the sample is t equals= and t 0.95=
using excel>addin>phstat>one sample test
we have
t Test for Hypothesis of the Mean | |
Data | |
Null Hypothesis m= | 999 |
Level of Significance | 0.05 |
Sample Size | 25 |
Sample Mean | 1006 |
Sample Standard Deviation | 22 |
Intermediate Calculations | |
Standard Error of the Mean | 4.4000 |
Degrees of Freedom | 24 |
t Test Statistic | 1.5909 |
Two-Tail Test | |
Lower Critical Value | -2.0639 |
Upper Critical Value | 2.0639 |
p-Value | 0.1247 |
Do not reject the null hypothesis |
The company is making acceptable light bulbs because the t-value for the sample is t =1.5909 and t0.95 = 2.0639
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