Question

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 = 0.49 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?

Answer: single proportions.

(a) What is the level of significance?
Answer: 0.01

State the null and alternate hypotheses.

H₀: μ ≠ 0.8; H₁: μ = 0.8

H₀: p = 0.8; H₁: p > 0.8    

H₀: μ = 0.8; H₁: μ ≠ 0.8

H₀: p = 0.8; H₁: p ≠ 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 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 unknown σ.

The Student's t, since we assume that x has a normal distribution with known 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.

Answer: There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.

Answer 1

a) single mean or one sample mean

Level of significance = 0.01

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

c) P-value = 0.0054

0.005 < P-value < 0.025

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

e) There is sufficient evidence at the 0.01 level to conclude that the toy company claim of 0.8 A is too low.