Do the following: a. Identify the hypothesis test as being...

Do the following: a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed. b. Find the $P$ -value. (See Figure $8-3$ on page $364 .$ ) c. Using a significance level of $\alpha=0.05,$ should we reject $H_{0}$ or should we fail to reject $H_{0} ?$ The test statistic of $z=-1.94$ is obtained when testing the claim that $p=3 / 8.$

Do the following:
a. Identify the hypothesis test as being two-tailed, left-tailed, or right-tailed.
b. Find the $P$ -value. (See Figure $8-3$ on page $364 .$ )
c. Using a significance level of $\alpha=0.05,$ should we reject $H_{0}$ or should we fail to reject $H_{0} ?$
The test statistic of $z=-1.94$ is obtained when testing the claim that $p=3 / 8.$

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical procedure used to evaluate assumptions about a population parameter based on sample data. It involves setting up a null hypothesis (typically a statement of no effect or status quo) and an alternative hypothesis, then using a test statistic to determine whether the observed result is sufficiently unlikely under the null hypothesis.

One?Tailed vs Two?Tailed Test

Determining whether a test is one?tailed or two?tailed is crucial because it affects the critical region(s) and the interpretation of the p-value. A two?tailed test is used when deviations in both directions from the hypothesized parameter are considered significant, while a one?tailed test examines deviation in a single specified direction.

Test Statistic

The test statistic is a standardized value calculated from sample data that is used to decide whether to reject the null hypothesis. For example, a z?statistic indicates how many standard errors the sample statistic is from the hypothesized value, thereby facilitating comparison with a standard normal distribution.

P-value

The p-value represents the probability of obtaining a test statistic at least as extreme as the one computed from the sample data, assuming that the null hypothesis is true. It provides a measure of the strength of evidence against the null hypothesis, with smaller values indicating stronger evidence for rejection.

Significance Level and Decision Rule

The significance level, denoted by ?, is a predefined threshold used to decide whether to reject the null hypothesis. If the p-value is less than or equal to ?, there is sufficient evidence to reject the null hypothesis; if it is greater, the decision is to fail to reject the null hypothesis. This rule helps control the probability of committing a Type I error.

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