An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 33
type K batteries and a sample of 39
type Q batteries. The type K batteries have a mean voltage of 8.60
, and the population standard deviation is known to be 0.348
. The type Q batteries have a mean voltage of 8.72
, and the population standard deviation is known to be 0.808
. 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.

Step 1 of 5 : State the null and alternative hypotheses for the test.