Consider the test of H0: μ=5. For each of the following, find the p -value of the test: a. Ha: μ

step 1 For this problem, we are told to consider the test of the null hypothesis that mu is equal to 5.

Consider the test of H0: μ=5. For each of the following,...

Consider the test of $H_{0}: \mu=5$. For each of the following, find the $p$ -value of the test:
a. $H_{\mathrm{a}}: \mu>5, z=3.16$
b. $H_{\mathrm{a}}: \mu<5, z=-3.16$
c. $H_{\mathrm{a}}: \mu \neq 5, z=3.16$

Key Concepts

Hypothesis Testing

Hypothesis testing is a statistical method used to make inferences about population parameters. It involves setting up a null hypothesis (a statement of no effect or status quo) and an alternative hypothesis (what the analyst wants to test), and then using sample data to decide whether to reject the null hypothesis.

Null and Alternative Hypotheses

The null hypothesis (H?) represents a default statement of no difference or no change, while the alternative hypothesis (H?) is what the researcher aims to support. The structure of these hypotheses guides the direction and type of the test, such as one-tailed or two-tailed.

Test Statistic

A test statistic is a standardized value calculated from sample data during a hypothesis test. It measures how far the sample data diverge from the null hypothesis. The z?statistic, for example, is used when the sampling distribution of the statistic is normal or approximately normal, and it provides a basis for calculating the p-value.

p-value

The p-value is the probability, under the assumption that the null hypothesis is true, of obtaining a test statistic at least as extreme as the one observed. It serves as a measure of the strength of evidence against the null hypothesis, with smaller p-values indicating stronger evidence to reject H?.

One-tailed Test

In a one-tailed test, the alternative hypothesis specifies a direction of interest (either greater than or less than). This means that the p-value is calculated based on the probability of the test statistic falling in one tail of the distribution.

Two-tailed Test

A two-tailed test is used when the alternative hypothesis does not specify a direction, only that there is a difference. Here, the p-value is computed by considering extreme values in both tails of the distribution. It is essentially twice the area in one tail corresponding to the observed test statistic.

Transcript

Please give Ace some feedback