Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis
The null hypothesis is a statement that there is no effect or no difference, and it serves as the default assumption in statistical testing. In this context, it posits that the standard deviation of the starting prices of the vehicles is $2900 or less. Failing to reject the null hypothesis means that there is not enough evidence to support a claim that the standard deviation exceeds this value.
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Statistical Significance
Statistical significance refers to the likelihood that a result or relationship is caused by something other than mere chance. In hypothesis testing, a result is considered statistically significant if the p-value is less than a predetermined threshold (commonly 0.05). When a decision fails to reject the null hypothesis, it suggests that the evidence is not strong enough to conclude that the standard deviation is greater than $2900.
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Parameters vs. Statistics
Type II Error
A Type II error occurs when a statistical test fails to reject a false null hypothesis, meaning that a real effect or difference is overlooked. In the context of the nonprofit organization, if the true standard deviation of starting prices is indeed greater than $2900, but the test fails to reject the null hypothesis, a Type II error has occurred. This highlights the importance of sample size and power in hypothesis testing to minimize such errors.
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