Assume that the significance level is α=0.05 ; use the given statement and find the P-value and critical values. (See Figure 8-4.) The test statistic of z=-2.00 is obtained when testing the claim that p<0.5

Name: Problem 18, Chapter 8: Essentials of Statistics
Uploaded: 2022-01-01 01:53:23-08:00
Duration: 1 min 10 s
Channel: Sarthi Patil
Description: Assume that the significance level is α=0.05 ; use the given statement and find the P-value and critical values. (See Figure 8-4.) The test statistic of z=-2.00 is obtained when testing the claim that p<0.5

Assume that the significance level is $\alpha=0.05 ;$ use the given statement and find the P-value and critical values. (See Figure 8-4.)
The test statistic of $z=-2.00$ is obtained when testing the claim that $p<0.5$

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to decide whether there is enough evidence in a sample of data to infer that a certain condition holds for the entire population. It involves formulating a null hypothesis that represents a baseline assumption and an alternative hypothesis that represents a claim to be tested against the null.

Null and Alternative Hypotheses

The null hypothesis (H0) typically represents a statement of no effect or status quo, while the alternative hypothesis (H1 or Ha) represents the claim or effect that the test aims to support. This framework guides the decision-making process in statistical inference.

Significance Level

The significance level, often denoted by ?, is the threshold used to determine whether the observed data are sufficiently unlikely under the null hypothesis. It represents the probability of committing a Type I error, which is rejecting the null hypothesis when it is actually true.

P-value

The P-value is the probability of obtaining a test statistic at least as extreme as the one observed, assuming that the null hypothesis is true. It provides a measure of the strength of the evidence against the null hypothesis; a smaller P-value indicates stronger evidence in favor of the alternative hypothesis.

Critical Values

Critical values define the cutoff point(s) on the distribution of the test statistic beyond which the null hypothesis is rejected. These values are determined based on the significance level and the nature of the test (one-tailed or two-tailed), delineating the boundaries of the rejection region.

One-Tailed Test

A one-tailed test evaluates the statistical significance of a result in only one direction. It is used when the research hypothesis predicts the direction of the effect (either greater than or less than a certain value), and the rejection region is located in one tail of the distribution.

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