Here are the essential concepts you must grasp in order to answer the question correctly.
Null Hypothesis (H0)
The null hypothesis (H0) is a statement that there is no effect or no difference, and it serves as the default assumption in hypothesis testing. In this case, H0 states that the population mean (μ) is less than or equal to 54. The goal of hypothesis testing is to determine whether there is enough evidence to reject this null hypothesis in favor of an alternative hypothesis.
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Confidence Intervals
A confidence interval is a range of values, derived from sample statistics, that is likely to contain the population parameter with a certain level of confidence (commonly 95%). Each interval provides an estimate of where the true population mean (μ) may lie. If a confidence interval does not include the value specified in the null hypothesis, it suggests that the null hypothesis may be rejected.
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Introduction to Confidence Intervals
Decision Rule for Hypothesis Testing
The decision rule in hypothesis testing involves comparing the confidence intervals to the null hypothesis. If the entire confidence interval lies above the value specified in H0 (in this case, 54), we reject H0. Conversely, if the interval includes or is below this value, we fail to reject H0. This rule helps in making informed decisions based on statistical evidence.
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