Question

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 32 type K batteries and a sample of 31 type Q batteries. The type K batteries have a mean voltage of 9.48, and the population standard deviation is known to be 0.293. The type Q batteries have a mean voltage of 9.85, and the population standard deviation is known to be 0.571. Conduct a hypothesis test for the conjecture that the mean voltage for these two types of batteries is different. Let μ1 be the true mean voltage for type K batteries and μ2 be the true mean voltage for type Q batteries. Use a 0.05 level of significance.

State the null and alternative hypotheses for the test.

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

Determine the decision rule for rejecting the null hypothesis H0. Round the numerical portion of your answer to two decimal places.

Make the decision for the hypothesis test (reject or fail to reject)

Find the P value for the hypothesis test. Round your answer to four decimal places.

Is there enough sufficient evidence or not enough?

Answer 1

Since , the population standard deviation is known.

Therefore , use normal distribution.

The null and alternative hypothesis is ,

The test is two-tailed test.

The test statistic is ,

The critical values are ,

Decision rule : Reject Ho , if Z-stat>1.96 or Z-stat<-1.96

Decision : Here , Z-stat=3.22>1.96

Therefore , reject Ho.

The p-value is ,

p-value=

; From standard normal distribution table

Decision : Here , p-value<0.05

Therefore , reject Ho.

Conclusion : There is enough evodence that the mean voltage for these two types of batteries is different.