Question

1.) Two different batteries are being considered for an industrial application. A random sample of 30 of Battery A produces a mean of 16.4 hours of useful voltage with a standard deviation of 3.2 hours. A sample of 30 of Battery B produces a mean of 17.1 hours with a standard deviation of 2.7 hours. The researcher is interested in finding evidence at the .05 level that Battery A has a different average than Battery B.

Which of the following pairs of hypotheses correctly characterizes the question of interest?

		H0: µA= µB HA: µA≠ µB
		H0: σA= σ B HA: σ A≠ σ B
		H0: pA= pB HA: pA≠ pB
		H0: µA≥ µB HA: µA< µB
		H0: σ A≤ σ B HA: σ A> σ B

2.) What's the value of the test statistic (using sample A as sample 1)?

3.) What is the p-value?

4.) What is the correct decision?

		Reject H0
		Don't Reject H0
		Reject HA
		Don't Reject HA

Answer 1

Since we want to know if Battery A has a different mean life than battery B

(1) The Hypothesis is Option 1

H0:

HA:

(2) Since s1/s2 = 3.2/2.7 = 1.185 (it lies between 0.5 and 2) we used the pooled standard deviation.

The degrees of freedom used is n1 + n2 - 2 = 30 + 30 -2 = 58 (since pooled variance is used)

The Test Statistic is given by

(3) The p value, 2 tailed at t = -0.92, df = 58; p value = 0.3614

(4) Since p value is > (0.05), Option 2: we don't reject H0.