Question 1

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

Accepted Answer

Null hypothesis is an existing theory or belief in statistics, which suggests that there is no significant difference between two groups being compared. Standard deviation, proportion, and alternative hypothesis are statistical concepts and tools and not theories or beliefs.

Question 2

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

Accepted Answer

The proper form of the hypotheses involves assuming that H0 (the null hypothesis) is true, and then testing whether the data provides enough evidence to reject it in favor of H1 (the alternative hypothesis). Therefore, option C is the correct choice, as H0 is indeed always assumed to be true in testing. Option A is incorrect because H0 is not proved true, but rather is either rejected or fails to be rejected based on the data. Option B is incorrect because failing to reject H0 does not necessarily prove H1 wrong - it simply means that there isn't enough evidence to reject H0. Option D is incorrect because H1 is a hypothesis that is proposed to replace H0, but it is not assumed to be true without evidence.

Question 3

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

Accepted Answer

A valid one-sample hypothesis test is typically structured as a null hypothesis (H0) and an alternative hypothesis (H1). The null hypothesis represents the status quo or the assumption that there is no significant difference or effect, while the alternative hypothesis represents the opposite or the claim that there is a significant difference or effect. Therefore, the null hypothesis should have an equal sign (=) to represent no significant difference or effect, and the alternative hypothesis should have a not-equal sign (≠) to represent a significant difference or effect. Choice D satisfies this requirement.

Question 4

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

Accepted Answer

The t-test statistic value of -1.76 falls in the left tail of the distribution with a level of significance of 0.10, indicating that the null hypothesis can be rejected. Therefore, the decision is to reject the null hypothesis.

Question 5

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

Accepted Answer

The initial step in conducting a hypothesis test is to clearly identify the population parameter of interest. This helps in formulating the null and alternative hypotheses, selecting an appropriate statistical test, and interpreting the results. Options A, B, and D are steps that come after identifying the population parameter.

Question 6

Use the data given below to answer the following question(s).
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 7

State how to increase the power of a test.
Compare and contrast the major types of hypothesis testing for one-sample tests
-For a one-tailed test, the critical value:

Accepted Answer

The critical value in a one-tailed test helps determine if the test statistic falls in the rejection region, which is crucial for deciding whether to reject the null hypothesis.

Question 8

Which of the following denotes the power of the test?

Accepted Answer

The power of the test is the probability of rejecting the null hypothesis when it is false. This is denoted by 1 - β, where β is the probability of a Type II error.

Question 9

State how to increase the power of a test.
Compare and contrast the major types of hypothesis testing for one-sample tests
-Which of the following is true about the rejection region?

Accepted Answer

The answer of State how to increase the power of...

Question 10

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

A Type II error occurs when the null hypothesis is not rejected when it is actually false. In this case, the null hypothesis was that the average company loss was $34,000, but it was not rejected even though the true average loss was $37,896.

Question 11

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

Accepted Answer

The power of the test measures the ability of a statistical test to correctly reject a false null hypothesis. A higher value of the power of the test indicates a higher probability of rejecting the null hypothesis correctly. A low value of the power of the test indicates a high probability of making a Type II error. Small sample sizes generate a low value of the power of the test because the sample statistics may not accurately represent the larger population. Therefore, B is the correct choice. Choice A and C are incorrect because a low value of the power of the test does not enable valid conclusions to be made or help in detecting small differences in sample statistics. Choice D is not relevant to the value of the power of the test.

Question 12

The confidence coefficient is denoted by:

Accepted Answer

The confidence coefficient is denoted by 1 - α. This is because it represents the probability of the interval containing the true population parameter. Therefore, the best choice is D.

Question 13

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 appropriate hypothesis test is a one-tailed test with the alternative hypothesis stating that the mean profit is greater than $6,710. Therefore, option B is the correct choice. options A, C, and D have the direction of the inequality symbols reversed or do not match the one-tailed nature of the test.

Question 14

Which of the following probabilities gives the confidence coefficient?

Accepted Answer

The confidence coefficient is the probability of not rejecting the null hypothesis when it is actually true. Therefore, choice D, P(not rejecting H0 | H0 is true), is the probability that gives the confidence coefficient.

Question 15

Type II error occurs when the test:

Accepted Answer

A Type II error occurs when a test fails to reject a null hypothesis that is actually false.

Question 16

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

Accepted Answer

The confidence coefficient is calculated as 1 minus the level of significance. Therefore, 1 - 0.03 = 0.97.

Question 17

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 when it is false, which is represented by P(rejecting H0 | H0 is false).

Question 18

Level of significance is the probability of:

Accepted Answer

Level of significance (also known as alpha) is the probability of incorrectly rejecting an actually true null hypothesis. This error is called a Type I error.

Question 19

State how to increase the power of a test.
Compare and contrast the major types of hypothesis testing for one-sample tests
-The average cost for the sample of 5 sales of a product is $\begin{array}{|l|l|l|}
\hline \text { Respondent } & \text { Gender } & \text { Breakfast Preference } \
\hline 1 & \text { Female } & \text { Fruits } \
\hline 2 & \text { Male } & \text { Cereal } \
\hline 3 & \text { Male } & \text { Milk } \
\hline 4 & \text { Female } & \text { Fruits } \\hline 5 & \text { Female } & \text { Milk } \
\hline 6 & \text { Male } & \text { Cereal } \
\hline 7 & \text { Male } & \text { Milk } \
\hline 8 & \text { Male } & \text { Milk } \
\hline 9 & \text { Female } & \text { Fruits } \\hline 10 & \text { Male } & \text { Fruits } \
\hline 11 & \text { Male } & \text { Cereal } \
\hline 12 & \text { Female } & \text { Cereal } \
\hline 13 & \text { Female } & \text { Milk } \
\hline 14 & \text { Male } & \text { Fruits } \
\hline 15 & \text { Female } & \text { Fruits } \
\hline
\end{array}$ = $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}} $. Here, $\bar{x} = 230$, $\mu_0 = 250$, $s = 17.50$, and $n = 5$. Plugging in these values, $ t = \frac{230 - 250}{17.50/\sqrt{5}} = -2.56 $.

Question 20

Explain how to draw a conclusion for one- and two-tailed hypothesis tests. LO2: Compare and contrast the major types of hypothesis testing for one-sample tests
-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, which is true for hypothesis testing.

Quiz 7: Statistical Inference