The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.34 A, with a sample standard deviation of s = 0.41 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.) State the null and alternate hypotheses. H0: μ ≠ 0.8; H1: μ = 0.8H0: μ = 0.8; H1: μ ≠ 0.8 H0: p = 0.8; H1: p ≠ 0.8H0: p ≠ 0.8; H1: p = 0.8H0: p = 0.8; H1: p > 0.8H0: μ = 0.8; H1: μ > 0.8 What sampling distribution will you use? What assumptions are you making? The Student's t, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with unknown σ. The standard normal, since we assume that x has a normal distribution with known σ.The Student's t, since we assume that x has a normal distribution with unknown σ. What is the value of the sample test statistic? (Round your answer to three decimal places.) (c) Find (or estimate) the P-value. P-value > 0.2500.125 < P-value < 0.250 0.050 < P-value < 0.1250.025 < P-value < 0.0500.005 < P-value < 0.025P-value < 0.005 Sketch the sampling distribution and show the area corresponding to the P-value.
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!
The Toylot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A) under a normal load. A sample of nine motors was tested, and it was found that the mean current was x = 1.34 A, with a sample standard deviation of s = 0.41 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)
State the null and alternate hypotheses.
What sampling distribution will you use? What assumptions are you making?
What is the value of the sample test statistic? (Round your answer to three decimal places.)
(c) Find (or estimate) the P-value.
Sketch the sampling distribution and show the area corresponding to the P-value.
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