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? (Round your answer to three decimal places.)


Find the P-value. (Round your answer to four decimal places.)

Answer 1

The sample test statistic = 3.159

The P-value = 0.0051

Explanation:

We are given that 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.

Let
`\mu` = average ampere (A) drawn by train under a normal load

So, Null Hypothesis,
`H_0` :
`\mu`
`\leq` 0.8 A {means that the Toylot claim is more than or equal to 0.8}

Alternate Hypothesis,
`H_A` :
`\mu` > 0.8 A {means that the Toylot claim of 0.8 A is too low}

The test statistics that will be used here is One-sample t test statistics as we don't know about population standard deviation;

T.S. =
`(\bar X-\mu)/((s)/(√(n) ) )` ~
`t_n_-_1`

where,
`\bar X` = sample mean current = 1.20 A

s = sample standard deviation = 0.42 A

n = sample of motors = 11

So, test statistics =
`(1.20-0.8)/((0.42)/(√(11) ) )` ~
`t_1_0`

= 3.159

The value of the sample test statistics is 3.159.

Now, P-value of the test statistics is given by the following formula;

P-value = P(
`t_1_0` > 3.159) = 0.0051 or 0.51%

Now at 1% significance level, the t table gives critical value of 2.764 at 10 degree of freedom for right-tailed test. Since our test statistics is more than the critical values of t as 3.159 > 2.764, so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region due to which we reject our null hypothesis.

Therefore, we conclude that the Toylot claim of 0.8 A is too low.