Question

Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is good, so a potential customer has decided to proceed with a purchase arrangement unless it can be demonstrated that the true average lifetime is shorter than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using computer software, which gave the following output. Variable n Mean StDev SEMean Z P-Value lifetime 50 738.44 38.20 5.40 -2.14 0.016 (a) Identify the form of the alternative hypothesis used for this problem and justify your answer. (b) What conclusion would be appropriate at the 0.05 significance level? At the 0.01 significance level? Explain your answer.

          Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is good, so a potential customer has decided to proceed with a purchase arrangement unless it can be demonstrated that the true average lifetime is shorter than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using computer software, which gave the following output.
Variable n Mean StDev SEMean Z P-Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
(a) Identify the form of the alternative hypothesis used for this problem and justify your answer.
(b) What conclusion would be appropriate at the 0.05 significance level? At the 0.01 significance level? Explain your answer.

Lightbulbs of a certain type are advertised as having an average lifetime of 750 hours. The price of these bulbs is good, so a potential customer has decided to proceed with a purchase arrangement unless it can be demonstrated that the true average lifetime is shorter than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined, and the appropriate hypotheses were tested using computer software, which gave the following output.
Variable n Mean StDev SEMean Z P-Value
lifetime 50 738.44 38.20 5.40 -2.14 0.016
(a) Identify the form of the alternative hypothesis used for this problem and justify your answer.
(b) What conclusion would be appropriate at the 0.05 significance level? At the 0.01 significance level? Explain your answer.

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