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:

Test Statistic

A value calculated from sample data that is used to test a hypothesis in statistics.

Normal

A type of statistical distribution where data is symmetrically distributed around the mean, known as the Gaussian distribution.

Confidence Interval

A range of values derived from sample statistics that is likely to contain the value of an unknown population parameter, with a specified level of confidence.

Population Proportion

The fraction or percentage of a population that exhibits a particular trait or characteristic.