Question

The output voltage for an electric circuit is specified to be 130. A sample of 40 independent readings on the voltage for this circuit gave a sample mean 128.6 and standard deviation 2.1. Test the hypothesis that the average output voltage is 130 against the alternative that it is less than 130. Use a test with level .05.

Answer 1

Answer:

We conclude that the average output voltage is less than 130.

Step-by-step explanation:

We are given that he output voltage for an electric circuit is specified to be 130.

A sample of 40 independent readings on the voltage for this circuit gave a sample mean 128.6 and standard deviation 2.1.

Let $\mu$ = average output voltage

SO, Null Hypothesis, $H_0$ : $\mu$ = 130   {means that the average output voltage is equal to 130}

Alternate Hypothesis, $H_A$ : $\mu$ < 130   {means that the average output voltage is less than 130}

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

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

where,  $\mu$ = sample mean output voltage = 128.6

             s = sample standard deviation = 2.1

             n = sample of independent reading = 40

So, test statistics  =  $\frac{128.6-130}{{\frac{2.1}{\sqrt{40} } } }$  ~ $t_3_9$

                               =  -4.216

Now at 0.05 significance level, the t table gives critical value of -1.685 at 39 degree of freedom for left-tailed test. Since our test statistics is less than the critical value of t as -4.216 < -1.685 so we have sufficient evidence to reject our null hypothesis as it will fall in the rejection region.

Therefore, we conclude that the average output voltage is less than 130.