In: Statistics and Probability
An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 4949 type K batteries and a sample of 38 type Q batteries. The type K batteries have a mean voltage of 9.16, and the population standard deviation is known to be 0.669. The type Q batteries have a mean voltage of 9.36, and the population standard deviation is known to be 0.194. 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 0.01 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.