Question 401195: A light-bulb manufacturer claims that the light bulbs produced by his company have an average life of 1200 hours. A consumer agency wishes to test this claim, against the alternative of fraudulent (i.e. the alternative that average life span is less than 1200 hours). A random sample of 16 bulbs is chosen from production and tested as the life times. The summary statistics turn out to X=1148.5 hours and S^2=12544.224. Based on these summary statistics, and at the α=0.05 level of significance
a) Obtain a 100(1-α )% confidence interval for the population mean ( μ ).
b) Formulate the corresponding hypothesis and test it.
How do I do This?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A light-bulb manufacturer claims that the light bulbs produced by his company have an average life of 1200 hours. A consumer agency wishes to test this claim, against the alternative of fraudulent (i.e. the alternative that average life span is less than 1200 hours).
A random sample of 16 bulbs is chosen from production and tested as the life times. The summary statistics turn out to X=1148.5 hours and S^2=12544.224. Based on these summary statistics, and at the α=0.05 level of significance
a) Obtain a 100(1-α )% confidence interval for the population mean ( μ ).
x-bar = 1148.5
ME = 1.753*112/sqrt(16) = 49.08
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95%CI: 1148.5-49.08 < u < 1148.5+49.08
95%CI: 1099.42 < u < 1197.58
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b) Formulate the corresponding hypothesis and test it.
Ho: u = 1200
Ha: u < 1200
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ts = 1148.5
t(1148.5) = (1148.5-1200)/[112/sqrt(16)] = -1.839
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p-value = P(t< -1.839 when df= 15) = 0.0429
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Conclusion: Since the p-value is < 5%, fail to reject Ho.
The test supports Ho at the 5% level of significance.
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Cheers,
Stan H.
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