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:

Each Quarter

A period of three months used in financial and business reporting.

Per Month

A term indicating the occurrence or measurement of something on a monthly basis.

Compounded Quarterly

Interest on an investment or loan calculated four times a year, adding each interest payment to the principal for future calculations.

Compounded Monthly

A system for calculating interest on a monthly cycle, including the original deposit or loan amount plus the accumulated interest from earlier cycles.