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 = 1.30 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.)

What are we testing in this problem?

single proportionsingle mean    

What is the level of significance?


State the null and alternate hypotheses.

H₀: μ = 0.8; H₁: μ ≠ 0.8H₀: p ≤ 0.8; H₁: p > 0.8    H₀: p ≠ 0.8; H₁: p = 0.8H₀: p = 0.8; H₁: p ≠ 0.8H₀: μ ≠ 0.8; H₁: μ = 0.8H₀: μ ≤ 0.8; H₁: μ > 0.8

What sampling distribution will you use? What assumptions are you making?

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 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.)


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.

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.

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.    

6.

Answer 1

The statistical software output for this problem is:

From above output:

What are we testing? Single mean

Level of significance = 0.01

Hypotheses: H0: μ ≤ 0.8; H1: μ > 0.8

Sampling distribution: Option D

Test statistic = 3.488

P-value < 0.005

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

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.