A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3.15 hours, with a sample standard deviation of 0.23 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 25 novices require a mean of 2.98 hours to complete the job. Assuming the population of times is normally distributed, and using the 0.01 level of significance, should we conclude that the new booklet is effective? Determine and interpret the p-value for the test
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!
1) A manufacturer of electronic kits has found that the mean time required for novices to assemble its new circuit tester is 3.15 hours, with a sample standard deviation of 0.23 hours. A consultant has developed a new instructional booklet intended to reduce the time an inexperienced kit builder will need to assemble the device. In a test of the effectiveness of the new booklet, 25 novices require a mean of 2.98 hours to complete the job. Assuming the population of times is
2) The International Council of Shopping Centers reports that the average teenager spends $57 during a shopping trip to the mall. The promotions director of a local mall has used a variety of strategies to attract area teens to his mall, including live bands and “teen appreciation days” that feature special bargains for this age group. He believes teen shoppers at his mall respond to his promotional efforts by shopping there more often and spending more when they do. Mall management decides to evaluate the promotions director’s success by surveying a simple random sample of 45 local teens and finding out how much they spent on their most recent shopping visit to the mall. Use a suitable hypothesis test in examining whether the mean mall shopping expenditure for teens in this area might be higher than for U.S. teens as a whole. Identify and interpret the p-value for the test. Using the 0.025 level of significance, what conclusion do you reach?
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