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 eleven motors was tested, and it was found that the mean current was x = 1.20 A, with a sample standard deviation of s = 0.42 A. Do the data indicate that the Toylot claim of 0.8 A is too low? (Use a 1% level of significance.)
What is the value of the sample test statistic?

Answer 1

Answer:

Test statistic = 3.1587

Step-by-step explanation:

We are given that the Toy-lot company makes an electric train with a motor that it claims will draw an average of only 0.8 ampere (A).

Also, a sample of eleven motors was tested, and it was found that the mean current was x = 1.20 A, with a sample standard deviation of s = 0.42 A.

So, Null Hypothesis, $H_0$ : $\mu$ = 0.8 { claim of 0.8 A is not low}

Alternate Hypothesis, $H_1$ : $\mu$ > 0.8 { claim of 0.8 A is too low}

Now, the test statistics used here will be;

           T.S. = $\frac{Xbar - \mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, X bar = sample mean = 1.20 A

                 s = sample standard deviation = 0.42 A

                 n = sample size = 11 motors

So, Test statistics = $\frac{1.20 - 0.8}{\frac{0.42}{\sqrt{11} } }$ ~ $t_1_0$

                             = 3.1587

At 1% level of significance, t table gives a critical value of 2.764 at 10 degree of freedom. Since our test statistics is higher than the critical value so we have sufficient evidence to reject null hypothesis .

Therefore, we conclude that Toy-lot claim of 0.8 A is too low.