Question 1

Which of the following denotes the power of the test?

Accepted Answer

The power of a statistical test is 1 - β, where β is the probability of making a Type II error (failing to reject a false null hypothesis). The power represents the test's ability to correctly reject a false null hypothesis.

Question 2

Which of the following propositions describes an existing theory or belief?

Accepted Answer

The null hypothesis is a theory or belief that is tested in a statistical hypothesis test.

Question 3

A manufacturer wishes to determine if the average profit from the sale of his product exceeds $6,710. Which of the following is the appropriate hypothesis test?

Accepted Answer

The null hypothesis (H0) typically represents a statement of no effect or no difference, or a statement of equality. It is the hypothesis that is initially assumed to be true. The alternative hypothesis (H1) is what you might believe to be true or hope to prove true. In this case, since the manufacturer wishes to determine if the average profit exceeds $6,710, the null hypothesis should reflect the opposite or the status quo (≤ $6,710), and the alternative hypothesis should reflect the manufacturer's hypothesis of interest (> $6,710).

Question 4

Identify the power of the test from the following probabilities.

Accepted Answer

The power of a test is the probability of correctly rejecting the null hypothesis (H0) when it is false, which is represented by "Prejecting H0 | H0 is false)."

Question 5

Which of the following is true about the rejection region?

Accepted Answer

The rejection region occurs in the tails of the sampling distribution of the test statistic.

Question 6

The average cost for the sample of 5 sales of a product is $\bar x$ = $230 and the sample standard deviation is s = $17.50. The hypothesized mean is ?0 = $250. Compute the value of the test statistic.

Accepted Answer

The test statistic is calculated using the formula $t = \frac{\bar x - \mu_0}{s/\sqrt{n}}$, where $\bar x$ is the sample mean, $\mu_0$ is the hypothesized mean, $s$ is the sample standard deviation, and $n$ is the sample size. Plugging in the given values, $t = \frac{230 - 250}{17.50/\sqrt{5}} = -2.56$.

Question 7

Which of the following is true about one-tailed and two-tailed tests?

Accepted Answer

For standard normal and t-distributions, lower-tail critical values are negative and upper-tail critical values are positive because these distributions are symmetric around a mean of zero.

Question 8

For a one-tailed test, the critical value:

Accepted Answer

The critical value in a one-tailed test determines the boundary of the rejection region. If the test statistic falls beyond this value, it indicates that the null hypothesis should be rejected, thus helping to decide whether the observed data falls into the region of rejection or not.

Question 9

Which of the following is true about the value of the power of the test?

Accepted Answer

The power of a test is the probability that it correctly rejects the null hypothesis when it is false. Small sample sizes tend to reduce the power of a test, making it less likely to detect a true effect when one exists.

Question 10

Type II error occurs when the test:

Accepted Answer

A Type II error occurs when a statistical test fails to reject a null hypothesis that is actually false, meaning the test indicates there is not enough evidence to support an alternative hypothesis when, in fact, the alternative is true.

Question 11

The confidence coefficient is denoted by:

Accepted Answer

The confidence coefficient is denoted by 1 - α, where α is the significance level. This means if you have a 95% confidence interval, α is 0.05, and thus the confidence coefficient is 1 - 0.05 = 0.95.

Question 12

Which of the following is true about determining the proper form of the hypotheses?

Accepted Answer

H0, or the null hypothesis, is always assumed to be true in the context of hypothesis testing. This assumption is made to facilitate the process of testing whether there is enough evidence to reject H0 in favor of the alternative hypothesis, H1.

Question 13

What is the confidence coefficient when the level of significance is 0.03?

Accepted Answer

The confidence coefficient is 1 minus the level of significance. So, for a level of significance of 0.03, the confidence coefficient is 1 - 0.03 = 0.9700.

Question 14

Which of the following probabilities gives the confidence coefficient?

Accepted Answer

The confidence coefficient is related to the probability of not rejecting the null hypothesis (H0) when it is true. This is because the confidence level (e.g., 95% confidence) is about how often we would expect to capture the true parameter if we were to repeat our sampling process many times under the same conditions.

Question 15

Use the data given below to answer the following questions).
In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76.
-What is the observed level of significance?

Accepted Answer

The answer of Use the data given below to answer...

Question 16

Which of the following is a Type I error?

Accepted Answer

A Type I error occurs when the null hypothesis is true, but the hypothesis test incorrectly rejects it.

Question 17

Which of the following is a valid one-sample hypothesis test?

Accepted Answer

The correct choice is D, where H0 (null hypothesis) states that the population parameter equals a constant, and H1 (alternative hypothesis) states that the population parameter does not equal that constant. This setup allows for a two-sided test, which is a common format for hypothesis testing.

Question 18

Which of the following is the initial step in conducting a hypothesis test?

Accepted Answer

Identifying the population parameter of interest is the initial step in conducting a hypothesis test, as it defines what you are trying to estimate or test about the population.

Question 19

Robin Inc. feared that the average company loss is running beyond $34,000. It initially conducted a hypothesis test on a sample extracted from its database. The hypothesis was formulated as H0: average company loss $34,000 vs. H1: average company loss > $34,000. The test resulted in favor of Robin Inc.'s loss not exceeding $34,000. Detailed study of company accounts later revealed that the average company loss had run up to $37,896. Which of the following errors were made during the hypothesis test?

Accepted Answer

Type II error occurs when the null hypothesis is not rejected when it is false. In this case, the hypothesis test incorrectly concluded that the average loss did not exceed $34,000, when in fact it was higher.

Question 20

Level of significance is the probability of:

Accepted Answer

The level of significance is the probability of making a Type I error, which is incorrectly rejecting a true null hypothesis.

Quiz 7: Statistical Inference

Which of the following denotes the power of the test?

Which of the following propositions describes an existing theory or belief?

A manufacturer wishes to determine if the average profit from the sale of his product exceeds $6,710. Which of the following is the appropriate hypothesis test?

Identify the power of the test from the following probabilities.

Which of the following is true about the rejection region?

The average cost for the sample of 5 sales of a product is $\bar x$ = $230 and the sample standard deviation is s = $17.50. The hypothesized mean is ?0 = $250. Compute the value of the test statistic.

Which of the following is true about one-tailed and two-tailed tests?

For a one-tailed test, the critical value:

Which of the following is true about the value of the power of the test?

Type II error occurs when the test:

The confidence coefficient is denoted by:

Which of the following is true about determining the proper form of the hypotheses?

What is the confidence coefficient when the level of significance is 0.03?

Which of the following probabilities gives the confidence coefficient?

Use the data given below to answer the following questions) . In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76. -What is the observed level of significance?

Which of the following is a Type I error?

Which of the following is a valid one-sample hypothesis test?

Which of the following is the initial step in conducting a hypothesis test?

Level of significance is the probability of:

Quiz 7: Statistical Inference

Which of the following denotes the power of the test?

Which of the following propositions describes an existing theory or belief?

A manufacturer wishes to determine if the average profit from the sale of his product exceeds $6,710. Which of the following is the appropriate hypothesis test?

Identify the power of the test from the following probabilities.

Which of the following is true about the rejection region?

The average cost for the sample of 5 sales of a product is xˉ\bar xxˉ = $230 and the sample standard deviation is s = $17.50. The hypothesized mean is ?0 = $250. Compute the value of the test statistic.

Which of the following is true about one-tailed and two-tailed tests?

For a one-tailed test, the critical value:

Which of the following is true about the value of the power of the test?

Type II error occurs when the test:

The confidence coefficient is denoted by:

Which of the following is true about determining the proper form of the hypotheses?

What is the confidence coefficient when the level of significance is 0.03?

Which of the following probabilities gives the confidence coefficient?

Use the data given below to answer the following questions) . In a lower one-tailed hypothesis test, chosen level of significance = 0.10, sample size = 55, and t- test statistic = -1.76. -What is the observed level of significance?

Which of the following is a Type I error?

Which of the following is a valid one-sample hypothesis test?

Which of the following is the initial step in conducting a hypothesis test?

Level of significance is the probability of:

The average cost for the sample of 5 sales of a product is $\bar x$ = $230 and the sample standard deviation is s = $17.50. The hypothesized mean is ?0 = $250. Compute the value of the test statistic.