An engineer is comparing voltages for two types of batteries (K and Q) using a sample of 57 type K batteries and a sample of 64 type Q batteries. The mean voltage is measured as 9.45 for the type K batteries with a standard deviation of 0.445 , and the mean voltage is 9.83 for type Q batteries with a standard deviation of 0.355 . 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 0.02 level of significance.
Step 1 of 4:
State the null and alternative hypotheses for the test.
Step 2 of 4:
Compute the value of the test statistic. Round your answer to two decimal places.
Step 3 of 4:
Determine the decision rule for rejecting the null hypothesis H0 . Round the numerical portion of your answer to two decimal places.
Step 4 of 4:
Make the decision for the hypothesis test.
Given
x̅1=9.45, σ1= 0.445, n1=57
x̅2=9.83, σ2=0.355, n2=64
Step 1 of 4:
two tailled test
Significance=0.02
Step 2 of 4:
Test Statistic(Z):
Step 3 of 4:
Rejection Rule: Reject Null hypothesi s, if p-value< Significance (0.02)
P-value=2*P(Z<-5.15)=0.0000
Here p-value< significance level(0.02)
Step 4 of 4:
p-value< significance level(0.02), reject the null hypothesis, there is enough evidence to support the claim.
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