What does the mean z-statistic measure?

The number of standard errors that the sample mean lies above or below the hypothesized mean.

What is a significance level, $\alpha$?

The preset probability of a Type I error under the null model.

What determines whether a hypothesis test is left-tailed, right-tailed, or two-tailed?

The direction specified by the alternative hypothesis.

How is the significance level allocated in a two-tailed test?

It is split equally, with $\alpha/2$ in each tail.

What does it mean to not reject a null hypothesis?

The sample evidence is insufficient to reject it at the selected significance level; this does not prove it true.

Business statisticsLesson 1 of 1 in the course Hypothesis Testing with One Sample

Choosing Distributions and Making Decisions in Hypothesis Tests

5 flashcards · 5 quiz questions · 5 match pairs · 5 fill-in sentences · English

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Summary

Hypothesis tests use probability distributions to judge whether sample results are plausible under a stated null hypothesis. The parameter being tested, what is known about the population, and the sample conditions determine which distribution to use.

A test about a population mean, $\mu$ , uses the sample mean, $\bar{x}$ , as its point estimate. The sampling distribution of $\bar{x}$ describes how sample means vary across repeated samples.

All flashcards

What does the mean z-statistic measure?: The number of standard errors that the sample mean lies above or below the hypothesized mean.
What is a significance level, $\alpha$ ?: The preset probability of a Type I error under the null model.
What determines whether a hypothesis test is left-tailed, right-tailed, or two-tailed?: The direction specified by the alternative hypothesis.
How is the significance level allocated in a two-tailed test?: It is split equally, with $\alpha/2$ in each tail.
What does it mean to not reject a null hypothesis?: The sample evidence is insufficient to reject it at the selected significance level; this does not prove it true.

Quiz questions

Assuming the null hypothesis is true, what does a p-value measure?Answer: The probability of a test statistic at least as extreme as the observed one in the alternative's direction.
A test rejects a null hypothesis that is actually true. What kind of error occurred?Answer: A Type I error.
For the alternative hypothesis $H_a: \mu < \mu_0$ , where is the rejection region?Answer: In the left tail of the reference distribution.
In a two-tailed z-test, which rule indicates rejection using the critical value $z_{\alpha/2}$ ?Answer: Reject when $|Z_c|>z_{\alpha/2}$ .
When selecting a test for a population mean, which information is relevant to choosing the procedure?Answer: Whether $\sigma$ is known, the sample size, and the applicable sampling assumptions.

Based on Introductory Business Statistics 2e by Alexander Holmes, Barbara Illowsky, Susan Dean (OpenStax), licensed CC BY 4.0. Adapted into a summary, flashcards and quizzes.

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