Math Problem Statement

The gas station owner insists that the mean wait time at his gas station is less than 2 minutes. Conduct a hypothesis test and state the conclusion.

Solution

The given problem involves conducting a hypothesis test regarding the mean wait time at a gas station. Here is the conclusion based on the context provided:

Conclusion: With 95% confidence, we fail to reject the null hypothesis. This means that we do not have enough evidence to conclude that the mean wait time at the gas station is less than 2 minutes. In other words, it is plausible that the mean wait time is 2 minutes or more.


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Related Questions:

  1. What are the possible reasons for failing to reject a null hypothesis in a hypothesis test?
  2. How can the sample size influence the outcome of this test?
  3. What does a confidence level of 95% imply in terms of hypothesis testing?
  4. How might the gas station owner reduce the mean wait time statistically or operationally?
  5. What are the consequences of a Type II error in this scenario?

Tip:

When failing to reject a null hypothesis, it does not mean the null hypothesis is true; it simply means there isn't enough evidence to support the alternative hypothesis. Always frame your conclusions carefully.

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Math Problem Analysis

Mathematical Concepts

Hypothesis Testing
Confidence Levels
Mean Comparison

Formulas

Test Statistic = (Sample Mean - Hypothesized Mean) / (Standard Deviation / √Sample Size)

Theorems

Central Limit Theorem
Null and Alternative Hypotheses

Suitable Grade Level

College or Advanced High School