The output voltage for a certain electric circuit is specified to be 130. A samp

Question

The output voltage for a certain electric circuit is specified to be 130. A sample of 10 independent reading on the voltage for this circuit gave a sample mean of 128.0 and a standard deviation of 2.1. Test the hypothesis that the average output voltage is 130. Use a 5% significance level. An automotive manufacturer believes that the variance of the gas mileage for its hybrid vehicles is 6. You work for an energy conservation agency and want to test this claim. You find that a random sample of the link's per gallon of 2H of the manufacturer's hybrid vehicles has a variance of 4.25. At alpha = 0.05 do you have enough evidence to reject the manufacturer's claim?

Explanation / Answer

(8)
Below are the null and alternate hypothesis,
H0: mu = 130
H1: mu < 130

Test statistics,
t = (128.6 - 130)/(2.1/sqrt(40)) = -4.22

p-value = 0.00007

As p-value is less than the significance level of 0.05, we reject the null hypothesis.

This means there are evidences which shows the output voltage mean is less than 130

(9)
Below are the null and alternate hypothesis,
H0: variance = 6
H1: variance not equals to 130

Test statistics,
T = (28 - 1)(4.25/6) = 19.125

Critical values: 2 /2,N-1 = 14.57
2 1-/2,N-1 = 43.19
Critical region: Reject H0 if T < 14.57 or T > 43.19

Here we fail to reject the null hypothesis.
This means there are not enough evidence to reject manufaturers claim.

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