Question

The Toylot company makes an electric train with a motor that it claims will draw an average of no more than 0.8 amps under a normal load. A sample of nine motors were tested, and it was found that the mean current was x = 1.32 amps, with a sample standard deviation of s = 0.43 amps. Perform a statistical test of the Toylot claim. (Use a 1% level of significance.)

a.) What are we testing in this problem?

-single proportion

-single mean

b.) What is the level of significance? ________

c.) 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: μ ≠ 0.8; H1: μ = 0.8

-H0: p = 0.8; H1: p ≠ 0.8

d.) 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 Student's t, 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 standard normal, since we assume that x has a normal distribution with unknown σ.

e.) What is the value of the sample test statistic? (Round your answer to three decimal places.) _____

f.)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

g.) Sketch the sampling distribution and show the area corresponding to the P-value.

h.) 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.

i.)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 no more than 0.8 amps is too low.

-There is insufficient evidence at the 0.01 level to conclude that the toy company claim of no more than 0.8 amps is too low.

Answer #1

**Solution:**

Given information:

n = 9, x̅ = 1.32, μ = 0.8, s = 0.43

a) -single mean

b) Level of significance α = 0.01

c) The null and alternate hypotheses

H0: μ ≤ 0.8; H1: μ > 0.8

d) -The Student's t, since we assume that x has a normal distribution with unknown σ.

e) Test statistic t = x̅ - μ/s/√n

= 1.32 - 0.8/0.43/√9

= 3.6279

f) P-value = 0.0067

0.005 < P-value < 0.025

h) -At the α = 0.01 level, we reject the null hypothesis and
conclude the data are statistically significant.

i) -There is insufficient evidence at the 0.01 level to conclude
that the toy company claim of no more than 0.8 amps is too low.

The Toylot company makes an electric train with a motor that it
claims will draw an average of no more than 0.8 amps under
a normal load. A sample of nine motors were tested, and it was
found that the mean current was x = 1.32 amps, with a
sample standard deviation of s = 0.41 amps. Perform a
statistical test of the Toylot claim. (Use a 1% level of
significance.)
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