The P-value for a hypothesis test is shown. Use the P-value...

The P-value for a hypothesis test is shown. Use the P-value to decide whether to reject $H_{0}$ when the level of significance is (a) $\alpha=0.01$ (b) $\alpha=0.05,$ and $(c) \alpha=0.10$.
$$P=0.0838$$

Key Concepts

Significance Level

The significance level, denoted by alpha (?), is a predetermined threshold used in hypothesis testing to decide when to reject the null hypothesis. It represents the probability of making a Type I error, which is the error of rejecting the true null hypothesis. Typical values for alpha are 0.01, 0.05, and 0.10.

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences or decisions about a population parameter based on sample data. It involves formulating a null hypothesis (H0) and an alternative hypothesis (Ha), and then using sample evidence to determine whether there is sufficient evidence to reject the null hypothesis in favor of the alternative.

P-value

The p-value is the probability of obtaining test results at least as extreme as the ones observed during the test, assuming that the null hypothesis is true. It quantifies the strength of evidence against the null hypothesis and helps in deciding whether to reject or not reject it based on how low or high the value is relative to a chosen threshold.

Decision Rule

The decision rule in hypothesis testing involves comparing the p-value to the significance level. If the p-value is less than or equal to the significance level, the null hypothesis is rejected, indicating that the sample provides sufficient evidence against it. If the p-value is greater, the null hypothesis is not rejected.

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