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Questions and Answers
What is the first step in specifying the null and alternative hypotheses?
What is the first step in specifying the null and alternative hypotheses?
- Find out the hypothesis concerning the issue under investigation (correct)
- Translate the words of the null hypothesis into a mathematical expression
- Write the two hypotheses as shown below
- Determine the direction of the alternative hypothesis
What is the null hypothesis represented as in mathematical form?
What is the null hypothesis represented as in mathematical form?
- H1 :μ 6¼ 0:17
- H0 :μ 6¼ 0:17
- H0 :μ 5 0:17 (correct)
- H1 :μ 5 0:17
What does the alternative hypothesis represent?
What does the alternative hypothesis represent?
- The mean concentration of cadmium of surface water is not equal to 0.17 mg/L (correct)
- The mean concentration of cadmium of surface water is exactly 0.17 mg/L
- The mean concentration of cadmium of surface water is greater than 0.17 mg/L
- The mean concentration of cadmium of surface water is less than 0.17 mg/L
What is the direction of the alternative hypothesis?
What is the direction of the alternative hypothesis?
What is the symbol used to represent the alternative hypothesis?
What is the symbol used to represent the alternative hypothesis?
What is the characteristic of the null and alternative hypotheses?
What is the characteristic of the null and alternative hypotheses?
What is the meaning of μ in the mathematical expressions of the hypotheses?
What is the meaning of μ in the mathematical expressions of the hypotheses?
What is the purpose of translating the words of the null hypothesis into a mathematical expression?
What is the purpose of translating the words of the null hypothesis into a mathematical expression?
What is the main goal of statistical hypothesis testing?
What is the main goal of statistical hypothesis testing?
What is the primary purpose of sampling in hypothesis testing?
What is the primary purpose of sampling in hypothesis testing?
What type of test is used for hypothesis testing regarding population proportions?
What type of test is used for hypothesis testing regarding population proportions?
When is a t-test used in hypothesis testing?
When is a t-test used in hypothesis testing?
What is the role of hypothesis testing in research?
What is the role of hypothesis testing in research?
What is being tested in the example given in the text?
What is being tested in the example given in the text?
What is the role of statistical techniques in research?
What is the role of statistical techniques in research?
What is the purpose of hypothesis testing in the example given in the text?
What is the purpose of hypothesis testing in the example given in the text?
What does the alternative hypothesis represent?
What does the alternative hypothesis represent?
What is the mathematical symbol for the alternative hypothesis?
What is the mathematical symbol for the alternative hypothesis?
What is the direction of the alternative hypothesis?
What is the direction of the alternative hypothesis?
What is the claim of the environmentalist?
What is the claim of the environmentalist?
What is the null hypothesis in the example?
What is the null hypothesis in the example?
How many steps are there to specify the null and alternative hypotheses?
How many steps are there to specify the null and alternative hypotheses?
What is the first step in specifying the null and alternative hypotheses?
What is the first step in specifying the null and alternative hypotheses?
What is the relationship between the null and alternative hypotheses?
What is the relationship between the null and alternative hypotheses?
What is the symbol for the probability of a type II error?
What is the symbol for the probability of a type II error?
What happens to type II error when type I error is decreased?
What happens to type II error when type I error is decreased?
What is the null hypothesis in the example of the mean concentration of cadmium?
What is the null hypothesis in the example of the mean concentration of cadmium?
What is a type I error in the context of the example of the mean concentration of cadmium?
What is a type I error in the context of the example of the mean concentration of cadmium?
What is a correct decision in the context of the example of the mean concentration of cadmium?
What is a correct decision in the context of the example of the mean concentration of cadmium?
What happens when we fail to reject a false null hypothesis in the context of the example of the mean concentration of cadmium?
What happens when we fail to reject a false null hypothesis in the context of the example of the mean concentration of cadmium?
What is the alternative hypothesis in the example of the mean concentration of cadmium?
What is the alternative hypothesis in the example of the mean concentration of cadmium?
What is the consequence of increasing type I error in the context of the example of the mean concentration of cadmium?
What is the consequence of increasing type I error in the context of the example of the mean concentration of cadmium?
What is the significance level selected in the procedure for identifying the critical and noncritical regions?
What is the significance level selected in the procedure for identifying the critical and noncritical regions?
What type of test is being conducted in the example?
What type of test is being conducted in the example?
What is the value of the critical value extracted for the one-tailed test with α = 0.05?
What is the value of the critical value extracted for the one-tailed test with α = 0.05?
What is the purpose of specifying the alternative hypothesis?
What is the purpose of specifying the alternative hypothesis?
What is the area shaded in Figure 1.2?
What is the area shaded in Figure 1.2?
What is the null hypothesis in the example?
What is the null hypothesis in the example?
What is the claim being examined in Example 1.6?
What is the claim being examined in Example 1.6?
Why is it necessary to assume that the data are normally distributed?
Why is it necessary to assume that the data are normally distributed?
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Study Notes
Introduction to Hypothesis Testing
- Researchers use statistical techniques to collect, analyze, summarize, and draw conclusions to gather information about populations under investigation.
- The purpose of statistical hypothesis testing is to make judgments about claims or issues using sample data to obtain correct decisions that guide researchers to accomplish their research objectives.
Hypothesis Testing
- Hypothesis testing is an important method to examine various claims or statements regarding different issues to support or deny the claims.
- It involves testing a hypothesis concerning population proportions, population means, and population variances.
- A Z-test is used for hypothesis testing regarding population proportions, and a Z-test or t-test can be used for population means.
- A chi-square test and F-test are used to test hypotheses concerning one and two variances.
Specifying Null and Alternative Hypotheses
- To specify null and alternative hypotheses, follow these steps:
- Identify the hypothesis concerning the issue under investigation.
- Translate the words of the null hypothesis into a mathematical expression.
- Translate the words of the alternative hypothesis into a mathematical expression.
- The null and alternative hypotheses are mutually exclusive and cannot occur at the same time.
Example: Testing a Claim about Concentration of Total Suspended Solids (TSSs)
- A researcher wants to test a claim that the mean concentration of TSSs in the surface water of a river is 465 mg/L.
- A sample should be selected from the river and tested for the concentration of TSSs, and the results summarized and analyzed to decide whether to support or reject the claim.
Example: Specifying Null and Alternative Hypotheses for a Left-Tailed Test
- The hypothesis is given in words: "the mean concentration of cadmium of surface water is less than 0.17 mg/L."
- The null and alternative hypotheses are:
- H0: μ ≤ 0.17
- H1: μ < 0.17
Critical and Noncritical Regions
- To identify the critical and noncritical regions, follow these steps:
- Specify the alternative hypothesis.
- Select the appropriate significance level (α).
- Extract the correct critical value from the standard normal table.
- The critical region is the area of rejection, and the noncritical region is the area of non-rejection.
Type I and Type II Errors
- Type I error: rejecting a true null hypothesis (α).
- Type II error: failing to reject a false null hypothesis (β).
- Type I and type II errors are inversely proportional; decreasing type I error increases type II error, and increasing type I error decreases type II error.
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