Preliminary Data Analyses Indicate That It Is Reasonable to Use $\bar { x } = 226,450$

question 48

Essay

Preliminary data analyses indicate that it is reasonable to use a t-test to carry out the specified hypothesis test. Performthe t-test using the P-value approach.
-A car manufacturer, Swanson, claims that the mean lifetime of one of its car engines is greater than 220,000 miles, which is the mean lifetime of the engine of a competitor. The mean lifetime for a random sample of 23 of the Swanson engines was $\bar { x } = 226,450$ miles with a standard deviation, s, of 11,500 miles. Test the Swanson's claim using a significance level of $\alpha = 0.01$ .

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Definitions:

Hypotheses

Statements made for the purpose of testing with statistical analysis, to see if there is enough evidence to support a particular belief or theory.

Significance Level

A threshold in hypothesis testing that determines the probability of rejecting a true null hypothesis, denoted as alpha (α).

Population Variance

The measure of the dispersion of all values in a population from the population mean.

Population Variance

A measure of the spread or dispersion within a set of data points in a population, indicating how much the data varies from the average.