Perform a One-Sample Z-Test for a Population Mean Using the P-Value

question 27

Essay

Perform a one-sample z-test for a population mean using the P-value approach. Be sure to state the hypotheses and thesignificance level, to compute the value of the test statistic, to obtain the P-value, and to state your conclusion. Also,assess the strength of the evidence against the null hypothesis.
-Last year, the mean running time for a certain type of flashlight battery was 8.5 hours. This year, the manufacturer has introduced a change in the production method which he hopes will increase the mean running time. A random sample of 40 of the new light bulbs was obtained and the mean running time was found to be 8.7 hours. Do the data provide sufficient evidence to conclude that the mean running time, µ, of the new light bulbs is larger than last year's mean of 8.5 hours? Perform the appropriate hypothesis test using a significance level of 5%. Assume that $\sigma$ = 0.5 hours.

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Definitions:

BCE

Before Common Era, a non-religious alternative to BC (Before Christ), used in the Gregorian calendar to denote years before the birth of Jesus.

Neolithic Construction

Refers to structures built during the Neolithic era, around 12,000 years ago, including monumental stone buildings and megalithic sites.

Northern Europe

A geographical and cultural region in Europe, typically including countries such as the United Kingdom, Scandinavia, and the Baltic states.

Henge

Prehistoric architectural structures consisting of a circular area enclosed by a bank and ditch, with internal features such as stone or wooden posts.