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.