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:

Early Behaviorists

Psychologists in the early 20th century who focused on studying observable behaviors and avoiding discussions of mental processes.

Biologically Determined

Traits or aspects of an individual that are genetically inherited rather than learned or developed through interaction with the environment.

Culturally Influenced

Shaped or affected by the customs, traditions, and social behaviors of a particular society or community.

Nature and Nurture

The debate and study of the relative influences of genetic inheritance (nature) and environmental factors (nurture) on human development.