Light bulbs of a certain type are advertised as having an average lifetime of 750 h. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined. The corresponding sample means and standard deviations are 738.44 and 38.2. Using 6-step process, carry out an appropriate hypothesis test at 5% significance level to answer the above research problem. Think of you are as one of the customers that buy this type of light bulbs. In the customer viewpoint which error is more critical? If you were to pick a significance level would you choose 1%, 5% or 10% significance level? Explain your choice
Continuous Probability Distributions
Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.
Normal Distribution
Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!
Light bulbs of a certain type are advertised as having an average lifetime of 750 h. The price of these bulbs is very favorable, so a potential customer has decided to go ahead with a purchase arrangement unless it can be conclusively demonstrated that the true average lifetime is smaller than what is advertised. A random sample of 50 bulbs was selected, the lifetime of each bulb determined. The corresponding sample means and standard deviations are 738.44 and 38.2.
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- Using 6-step process, carry out an appropriate hypothesis test at 5% significance level to answer the above research problem.
- Think of you are as one of the customers that buy this type of light bulbs. In the customer viewpoint which error is more critical? If you were to pick a significance level would you choose 1%, 5% or 10% significance level? Explain your choice
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