Question

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 89 type K batteries and a sample of 103 type Q batteries. The type K batteries have a mean voltage of 8.51, and the population standard deviation is known to be 0.312. The type Q batteries have a mean voltage of 8.77, and the population standard deviation is known to be 0.779. 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.

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

Step 2 of 5: Compute the value of the test statistic. Round your answer to two decimal places.

Step 3 of 5: Find the p-value associated with the test statistic. Round your answer to four decimal places.

Step 4 of 5: reject or fail to reject the null hypothersis?

Step 5 of 5: do we have sufficient evidence or insufficient evidence?

Answer 1

The statistical software output for this problem is :

H₀ : μ₁ - μ₂ = 0 , H_A : μ₁ - μ₂ ≠ 0

Test statistics = -3.11

P-value = 0.0019

Reject the null hypothesis

sufficient evidence