Question

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 37 type K batteries and a sample of 58 type Q batteries. The type K batteries have a mean voltage of 8.54, and the population standard deviation is known to be 0.225. The type Q batteries have a mean voltage of 8.69, and the population standard deviation is known to be 0.725. 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 0.1 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 : Make the decision for the hypothesis test: Reject Null Hypothesis or Fail to Reject Null Hypothesis

Step 5 of 5 : State the conclusion of the hypothesis test: There is sufficient evidence to support the claim or There is not sufficient evidence to support the claim.

PLEASE DO NOT ANSWER UNLESS YOU ARE CONFIDENT YOUR ANSWER WILL BE CORRECT.

Answer 1

Step 1

To Test :-

H0 :- µ1 = µ2
H1 :- µ1 ≠ µ2

Step 2

Test Statistic :-


Z = -1.47

Step 3

P value = P ( Z < 1.4687 ) = 0.1419 ( From Z table )

Step 4

Decision based on P value
Reject null hypothesis if P value < α = 0.1 level of significance
Since 0.1419 > 0.1 ,hence we reject null hypothesis
Result :- We fail to reject null hypothesis

Step 5

There is not sufficient evidence to support the claim.