Question

An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 97 type K batteries and a sample of 70 type Q batteries. The type K batteries have a mean voltage of 9.09, and the population standard deviation is known to be 0.385. The type Q batteries have a mean voltage of 9.34, and the population standard deviation is known to be 0.523. 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:

Make the decision for the hypothesis test. (Reject or Fail Reject Null Hypothesis)

Step 5 of 5:

Make the decision for the hypothesis test. (There is sufficient evidence to support the hypothesis, or there is not)

Answer 1

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


Z = -3.3909

Test Criteria :-
Reject null hypothesis if


Result :- Reject Null Hypothesis

Decision based on P value
P - value = P ( Z < 3.3909 ) = 0.0007
Reject null hypothesis if P value <    level of significance
P - value = 0.0007 < 0.05 ,hence we reject null hypothesis
Conclusion :- Reject null hypothesis

There is sufficient evidence to support the hypothesis that two types of batteries is different.