Q: Which of the following scenarios describes a left-tailed test?

The alternative hypothesis is $$H_a: \\mu \u003c \\mu_0$.

Q: Which formula is used to calculate the test statistic for a one-mean z-test?

$$z = \\frac{\\bar{x} - \\mu_0$}{\\sigma / \\sqrt{n}}$$

Q: Which of the following statements is true regarding the relationship between Type I and Type II error probabilities?

Increasing the significance level $$\\alpha$$ decreases the probability of a Type II error.

Question 1

Which of the following best describes the null hypothesis ($$H_0) in $$hypothesis testing?

Accepted Answer

It is a statement that there is no effect or difference, and is denoted as $$H_0$$: \mu = \$$mu_0.$$

Question 2

What is a Type I Error in hypothesis testing?

Accepted Answer

Rejecting the null hypothesis when it is true.

Question 3

If the significance level $$\alpha is $$increased, what happens to the probability of a Type I Error?

Accepted Answer

It increases.

Question 4

Which of the following scenarios describes a left-tailed test?

Accepted Answer

The alternative hypothesis is $$H_a: \mu \u003c \mu_0$.

Question 5

A snack-food company tests whether the mean weight of its pretzel bags is 454g. If the true mean is 454g, but the results of the sample lead to the conclusion that $$\mu \neq 454g$$, what type of error has occurred?

Accepted Answer

Type I Error

Question 6

Which formula is used to calculate the test statistic for a one-mean z-test?

Accepted Answer

$$z = \frac{\bar{x} - \mu_0$}{\sigma / \sqrt{n}}$$

Question 7

For a two-tailed test at the 5% significance level ($$\alpha = 0.05$$), what are the critical values?

Accepted Answer

$$z = \pm 1.96$$

Question 8

When should the one-sample z-test be used for small samples ($$n \u003c 15$$)?

Accepted Answer

When the variable under consideration is normally distributed or very close to being so, with no outliers.

Question 9

What is the rejection region for a right-tailed test at $$\alpha = 0.05$$?

Accepted Answer

$$z \u003e 1.645$$

Question 10

Which of the following statements is true regarding the relationship between Type I and Type II error probabilities?

Accepted Answer

Increasing the significance level $$\alpha$$ decreases the probability of a Type II error.

Question 11

A researcher performs a hypothesis test and finds that the test statistic falls in the rejection region. What should the researcher conclude?

Accepted Answer

Reject the null hypothesis.

Question 12

Which of the following is a correct conclusion for a hypothesis test if $$H_0 is $$rejected?

Accepted Answer

There is enough evidence to support $$H_a$$ and the test results are significant.

Question 13

In a hypothesis test, what does the critical value represent?

Accepted Answer

The value that separates the acceptance and rejection regions for $$H_0.$$

Question 14

A company wants to test if the mean price of its product has increased from last year. Which alternative hypothesis should be used?

Accepted Answer

$$H_a: \mu \u003e \mu_0$

Question 15

Which of the following is NOT a step in performing a one-mean z-test?

Accepted Answer

Calculate the sample variance.

Question 16

For moderate samples ($$n = 15 to$$ $$n = 30) $$with no outliers, which test is appropriate?

Accepted Answer

One-sample z-test

Question 17

If the sample size is large ($$n \u003e 30) $$and outliers are present, what should you do before using the z-test?

Accepted Answer

Remove the outliers and run the test again.

Question 18

Which region is called the acceptance region in hypothesis testing?

Accepted Answer

The region where the test statistic does not lead to rejection of $$H_0.$$

Question 19

What is the main purpose of performing a hypothesis test for a population mean?

Accepted Answer

To decide whether there is enough evidence to reject the null hypothesis in favor of the alternative hypothesis.

Hypothesis Testing and the One-Mean z-Test: Structured Study Notes

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