Question

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 8484 type K batteries and a sample of 6666 type Q batteries. The type K batteries have a mean voltage of 8.698.69, and the population standard deviation is known to be 0.1240.124. The type Q batteries have a mean voltage of 8.808.80, and the population standard deviation is known to be 0.6200.620. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1μ1 be the true mean voltage for type K batteries and μ2μ2 be the true mean voltage for type Q batteries. Use a 0.010.01 level of significance.

1

State the null and alternative hypotheses for the test.

2

Compute the value of the test statistic. Round your answer to two decimal places.

3  

Find the p-value associated with the test statistic. Round your answer to four decimal places.

4    

Make the decision for the hypothesis test.

5    

State the conclusion of the hypothesis test.

Answer 1

1)

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ1 = μ2
Alternative Hypothesis, Ha: μ1 ≠ μ2

2)

Pooled Variance
sp = sqrt(s1^2/n1 + s2^2/n2)
sp = sqrt(0.015376/84 + 0.3844/66)
sp = 0.0775

Test statistic,
z = (x1bar - x2bar)/sp
z = (8.69 - 8.8)/0.0775
z = -1.42

3)

P-value Approach
P-value = 0.1556

4)

As P-value >= 0.01, fail to reject null hypothesis.

5)

There is not sufficient evidence to conclude that the mean voltage for these two types of batteries is different.