Conduct a full hypothesis test and determine if the given claim is supported or not supported at the 0.05 significance level. Round all amounts and standard scores to two decimal places.
-In the past, the mean running time for a certain type of flashlight battery has been 8.7 hours. The manufacturer has introduced a change in the production method which he hopes has increased the mean running time. The mean running time for a random sample of 40 light bulbs was 8.9 hours. Test whether the claim that the mean running time of all light bulbs has increased from the previous mean of 8.7 hours is supported or not supported. Assume that ? = 0.5 hours.
A)not supported
B)supported

Question

Quizplus · Accepted Answer

The null hypothesis is that the mean running time is 8.7 hours, and the alternative hypothesis is that it is greater than 8.7 hours. Using a one-sample z-test, the z-score is calculated as (8.9 - 8.7) / (0.5/√40) = 2.53. The critical z-value for a 0.05 significance level (one-tailed) is approximately 1.645. Since 2.53 > 1.645, we reject the null hypothesis, supporting the claim that the mean running time has increased.

Conduct a Full Hypothesis Test and Determine If the Given