Applications of Hypothesis Testing for Environmental Science

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Questions and Answers

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?

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?

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?

Greater than or less than 0.17 mg/L Signup and view all the answers

What is the symbol used to represent the alternative hypothesis?

≠ Signup and view all the answers

What is the characteristic of the null and alternative hypotheses?

They are mutually exclusive Signup and view all the answers

What is the meaning of μ in the mathematical expressions of the hypotheses?

Population mean Signup and view all the answers

What is the purpose of translating the words of the null hypothesis into a mathematical expression?

To test the hypothesis using statistical methods Signup and view all the answers

What is the main goal of statistical hypothesis testing?

To make judgments regarding a claim or issue Signup and view all the answers

What is the primary purpose of sampling in hypothesis testing?

To select a representative sample from the population Signup and view all the answers

What type of test is used for hypothesis testing regarding population proportions?

Z-test Signup and view all the answers

When is a t-test used in hypothesis testing?

When the sample size is small Signup and view all the answers

What is the role of hypothesis testing in research?

To guide researchers in achieving research objectives Signup and view all the answers

What is being tested in the example given in the text?

The concentration of TSSs in the surface water of a river Signup and view all the answers

What is the role of statistical techniques in research?

To analyze and summarize data Signup and view all the answers

What is the purpose of hypothesis testing in the example given in the text?

To support or deny the claim regarding the concentration of TSSs Signup and view all the answers

What does the alternative hypothesis represent?

The opposite of the null hypothesis Signup and view all the answers

What is the mathematical symbol for the alternative hypothesis?

H1 :μ. 0:17 Signup and view all the answers

What is the direction of the alternative hypothesis?

Greater than 0.17 mg/L Signup and view all the answers

What is the claim of the environmentalist?

The mean concentration of cadmium is less than 0.17 mg/L Signup and view all the answers

What is the null hypothesis in the example?

The mean concentration of cadmium is not less than 0.17 mg/L Signup and view all the answers

How many steps are there to specify the null and alternative hypotheses?

3 steps Signup and view all the answers

What is the first step in specifying the null and alternative hypotheses?

Find out the hypothesis concerning the issue under investigation Signup and view all the answers

What is the relationship between the null and alternative hypotheses?

They are mutually exclusive Signup and view all the answers

What is the symbol for the probability of a type II error?

β Signup and view all the answers

What happens to type II error when type I error is decreased?

It increases Signup and view all the answers

What is the null hypothesis in the example of the mean concentration of cadmium?

μ = 0.17 Signup and view all the answers

What is a type I error in the context of the example of the mean concentration of cadmium?

Rejecting a true null hypothesis Signup and view all the answers

What is a correct decision in the context of the example of the mean concentration of cadmium?

Not rejecting a true null hypothesis Signup and view all the answers

What happens when we fail to reject a false null hypothesis in the context of the example of the mean concentration of cadmium?

A type II error occurs Signup and view all the answers

What is the alternative hypothesis in the example of the mean concentration of cadmium?

μ ≠ 0.17 Signup and view all the answers

What is the consequence of increasing type I error in the context of the example of the mean concentration of cadmium?

Type II error decreases Signup and view all the answers

What is the significance level selected in the procedure for identifying the critical and noncritical regions?

0.05 Signup and view all the answers

What type of test is being conducted in the example?

Right-tailed test Signup and view all the answers

What is the value of the critical value extracted for the one-tailed test with α = 0.05?

1.645 Signup and view all the answers

What is the purpose of specifying the alternative hypothesis?

To identify the critical and noncritical regions Signup and view all the answers

What is the area shaded in Figure 1.2?

The critical region Signup and view all the answers

What is the null hypothesis in the example?

H0: μ = 0.17 Signup and view all the answers

What is the claim being examined in Example 1.6?

The mean concentration of cadmium is less than 0.17 mg/L Signup and view all the answers

Why is it necessary to assume that the data are normally distributed?

To conduct the right-tailed test Signup and view all the answers

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:
1. Identify the hypothesis concerning the issue under investigation.
2. Translate the words of the null hypothesis into a mathematical expression.
3. 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:
1. Specify the alternative hypothesis.
2. Select the appropriate significance level (α).
3. 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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Description

This quiz explores the use of statistical techniques, specifically hypothesis testing, in collecting and analyzing data to draw conclusions about environmental science.

Applications of Hypothesis Testing for Environmental Science

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Questions and Answers

What is the first step in specifying the null and alternative hypotheses?

What is the null hypothesis represented as in mathematical form?

What does the alternative hypothesis represent?

What is the direction of 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 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 main goal of statistical hypothesis testing?

What is the primary purpose of sampling in hypothesis testing?

What type of test is used for hypothesis testing regarding population proportions?

When is a t-test used in hypothesis testing?

What is the role of hypothesis testing in research?

What is being tested in the example given in the text?

What is the role of statistical techniques in research?

What is the purpose of hypothesis testing in the example given in the text?

What does the alternative hypothesis represent?

What is the mathematical symbol for the alternative hypothesis?

What is the direction of the alternative hypothesis?

What is the claim of the environmentalist?

What is the null hypothesis in the example?

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 relationship between the null and alternative hypotheses?

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 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 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 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 significance level selected in the procedure for identifying the critical and noncritical regions?

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 purpose of specifying the alternative hypothesis?

What is the area shaded in Figure 1.2?

What is the null hypothesis in the example?

What is the claim being examined in Example 1.6?

Why is it necessary to assume that the data are normally distributed?

Study Notes

Introduction to Hypothesis Testing

Hypothesis Testing

Specifying Null and Alternative Hypotheses

Example: Testing a Claim about Concentration of Total Suspended Solids (TSSs)

Example: Specifying Null and Alternative Hypotheses for a Left-Tailed Test

Critical and Noncritical Regions

Type I and Type II Errors

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