Chapter 11- Testing A Claim



Chapter 11- Testing A Claim

11.1 Significance Tests: The Basics (pages 684-704)

1. What is a null hypothesis?

A statement being tested. (The status quo statement, it suggests no change or no difference.)

Notated as Ho.

2. What is an alternative hypothesis?

The claim about a population that we are trying to find evidence for. (Statement that suggests that something has changed or is different than expected.) Notated as Ha.

3. What conditions should be satisfied before significance testing?

SRS, Normality, Independence

4. In statistics, what is meant by the p-value ?

The probability that the observed outcome would take a value as extreme as or more extreme than that actually observed.

5. If a p-value is small, what do we conclude about the null hypothesis ?

There is more evidence against the null hypothesis, Ho. A low p-value means the observed result is unlikely to occur by chance if the null hypothesis, Ho, is true.

6. If a p-value is large, what do we conclude about the null hypothesis ?

It means there is not enough evidence against the null hypothesis, Ho,. There is no reason not to believe the null hypothesis.

7. How small should the p-value be in order to claim that a result is statistically significant?

The p-value needs to be as small as or smaller than the alpha, α, level. The alpha level depends on our significance level.

8. What does statistically significant mean?

This means that something, an event, is unlikely to happen by chance.

11.2 Carrying Out Significance Tests (pages 704-716)

1. Explain the difference between a one-sided alternative hypothesis and a two-sided alternative hypothesis?

One sided means a specific direction such as greater than or less than. A two-sided alternative means either direction, greater than or less than.

1-sided < or > 2 sided ≠

2. Write the steps to follow for significance testing.

11.3 Use and Abuse of Tests ( pages 716-722)

1. What does a test statistic estimate? The degree of evidence provided by a sample against the null hypothesis, Ho.

2. What is meant by a significance level ?

The level that is “good enough” to be believed. 95% significance level means 5% of not being true.

3. Significance tests are not always valid. What are some factors that can invalidate a test?

• Faulty data collection

• Outliers in the data

• Testing a hypothesis after sampling (using results to meet your needs/wants)

• Testing a sample that is too small

11,4 Using Inference to Make Decisions (pages 722-739)

1. Explain the difference between a Type I error and a Type II error.

Type 1: If you reject Ho, when the Ho is actually true.

Type 2: If you fail to reject Ho , when Ho is false.

2. What is the relationship between the significance level α and the probability of a Type I error?

The significance level, α ( alpha), of any fixed level test is the probability of a Type 1 error.

Alpha, α, is the probability that the test will reject the Ho, when in fact the Ho is true.

3. Describe how to calculate the Power of a significance test?

Power: the probability that a fixed level, α, significance test will reject Ho , when a particular alternative value of the parameter is true, is called power.

The power of a test against any alternative is 1 minus the probability of a Type 2 error, β.

(1 – β)

4. How can the Power of a test be increased? Which of the methods are the most feasible?

• Increase α – A test at a 5% significance level will have a greater chance of rejecting the alternative than a 1% test because the strength of evidence required is less.

• Increase sample size – More data will provide more information about [pic] , so we have a better chance of distinguishing values of µ.

• Decrease σ – the smaller the deviation the more precise our estimate

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Key Vocabulary:

Null hypothesis Alternate hypothesis P-Value Statistical significance

1-sided 2-sided test statistic significance level Type I Type II

Power α β σ

Calculator Skills:

z-test z-interval

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