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= 1.22 A, with a sample standard deviation of s = 0.44 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)

1. What are we testing in this problem?
a. single proportion
b. single mean

2. What is the level of significance?
3. State the null and alternate hypotheses.

4. What sampling distribution will you use? What assumptions are you making?
a. The Student's t, since we assume that x has a normal distribution with known σ
b. The standard normal, since we assume that x has a normal distribution with known σ.
c. The standard normal, since we assume that x has a normal distribution with unknown σ.
d. The Student's t, since we assume that x has a normal distribution with unknown σ.

Answer 1

1. B

Explanation:

1. We are testing against the null hypothesis which is a single mean that sauce the average load is 0.8A

2. The level of significance is 1% (99% confidence interval)

3. The null hypothesis: u = 0.8

Alternative hypothesis: u =/ 0.8

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

5. Using the formula t = (x - u) / σ√n

Where x = 1.22 u = 0.8 σ = 0.44 n = 9

t = (1.22-0.8) / 0.44√9

t = 0.42/(0.44x3)

t = 0.42/1.32

t = 0.318

P value for 0.318 at 1% level of significance at 8 degree of freedom is 0.7586. Since our p value here is greater than 0.01, we can convince that there is not enough statistical evidence that indicate that the Toylot claim of 0.8 A is too low.