he 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.) What are we testing in this problem? single mean single proportion (a) What is the level of significance? State the null and alternate hypotheses. H0: p = 0.8; H1: p ≠ 0.8 H0: p = 0.8; H1: p > 0.8 H0: μ = 0.8; H1: μ ≠ 0.8 H0: μ ≠ 0.8; H1: μ = 0.8 H0: p ≠ 0.8; H1: p = 0.8 H0: μ = 0.8; H1: μ > 0.8 (b) What sampling distribution will you use? What assumptions are you making? The standard normal, 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 Student's t, 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.)
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.)
What are we testing in this problem?
single mean
single proportion
(a) What is the level of significance?
State the null and alternate hypotheses.
H0: p = 0.8; H1: p ≠ 0.8
H0: p = 0.8; H1: p > 0.8
H0: μ = 0.8; H1: μ ≠ 0.8
H0: μ ≠ 0.8; H1: μ = 0.8
H0: p ≠ 0.8; H1: p = 0.8
H0: μ = 0.8; H1: μ > 0.8
(b) What sampling distribution will you use? What assumptions are you making?
The standard normal, since we assume that x has a
The standard normal, since we assume that x has a normal distribution with unknown σ.
The Student's t, 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 >0.250
0.125 < P-value <0.250
0.050 < P-value < 0.125
0.025 < P-value < 0.050
0.005 < P-value <0.025
P-value < 0.005
Sketch the sampling distribution and show the area corresponding to the P-value.
(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?
At the α = 0.01 level, we reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.01 level, we reject the null hypothesis and conclude the data are not statistically significant.
At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are statistically significant.
At the α = 0.01 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
(e) Interpret your conclusion in the context of the application.
There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.
There is insufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.
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