An electrical company claims that the lives of the light bulbs it manufactures are normally distributed with a mean of 1,000 hours and standard deviations of 100 hours. Test if the sample mean is significantly different from 1000 hours, if a random sample of 100 bulbs produced by this company has a mean of 980 hours. Using 5% level of significance, p value obtained was 0.045500124.

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compute using the 5-step solution

Step 1: State the Hypothesis Ha: # 100 hrs
Ho:i = 100 hrs
Step 2: Level of Significance a = 0.05 (Two – tailed)
Z- test
f = 100 hrs
H= 980 hrs
n= 100 bulbs
o = 100 hrs
Step 3: Test to be used
Step 4: Calculations
100 – 980
2
100/V100
From the normal probability distribution table
P(z = 2) = 0.0455
Rejection Region: P(Z)s 0.025 or P(Z) 2 0.975
Acceptance Region: 0.025 < P(Z) < 0.0975
Step 5: Conclusion
Since P(z = 2) = 0.0455 is within the acceptance region, we accept the
nul hypothesis.
| Therefore the sample mean is significantly different from 1000 hours
Transcribed Image Text:Step 1: State the Hypothesis Ha: # 100 hrs Ho:i = 100 hrs Step 2: Level of Significance a = 0.05 (Two – tailed) Z- test f = 100 hrs H= 980 hrs n= 100 bulbs o = 100 hrs Step 3: Test to be used Step 4: Calculations 100 – 980 2 100/V100 From the normal probability distribution table P(z = 2) = 0.0455 Rejection Region: P(Z)s 0.025 or P(Z) 2 0.975 Acceptance Region: 0.025 < P(Z) < 0.0975 Step 5: Conclusion Since P(z = 2) = 0.0455 is within the acceptance region, we accept the nul hypothesis. | Therefore the sample mean is significantly different from 1000 hours
An electrical company claims that the lives of the light bulbs it
manufactures are normally distributed with a mean of 1,000 hours and
standard deviations of 100 hours. Test if the sample mean is significantly
different from 1000 hours, if a random sample of 100 bulbs produced by
this company has a mean of 980 hours. Using 5% level of significance, p -
value obtained was 0.045500124.
Transcribed Image Text:An electrical company claims that the lives of the light bulbs it manufactures are normally distributed with a mean of 1,000 hours and standard deviations of 100 hours. Test if the sample mean is significantly different from 1000 hours, if a random sample of 100 bulbs produced by this company has a mean of 980 hours. Using 5% level of significance, p - value obtained was 0.045500124.
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