Statistical Hypothesis Testing

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Questions and Answers

What is the term for a statement about the value of a population parameter?

Parameter estimate

Point estimate

Alternative hypothesis

Null hypothesis (correct)

Which error occurs if we incorrectly reject a true null hypothesis?

Standard deviation error

Type-I error (correct)

Type-II error

Sampling error

Is hypothesis testing also known as significance testing?

Sometimes

Only in specific cases

Yes (correct)

In hypothesis testing, what do we assess regarding the sample mean and the population mean?

Whether they are equal Signup and view all the answers

What is the main purpose of hypothesis testing?

To determine whether a statistical result is significant Signup and view all the answers

What is a statement made about a population for testing purposes called?

Hypothesis Signup and view all the answers

In a criminal trial, a Type II error happens when:

A guilty person is set free Signup and view all the answers

What occurs when we do not reject a false null hypothesis?

Type-II error Signup and view all the answers

If the null hypothesis is false, which hypothesis is accepted?

Alternative Hypothesis Signup and view all the answers

Which error occurs when we accept a true null hypothesis?

Correct decision Signup and view all the answers

What is the first step in hypothesis testing?

Define the null and alternative hypotheses Signup and view all the answers

In hypothesis testing, what is the purpose of the p-value?

To compare against the level of significance for decision making Signup and view all the answers

What does a Type I error represent in hypothesis testing?

Rejecting a true null hypothesis Signup and view all the answers

Which statement is the null hypothesis (H0) for the smoking rate example?

There is no difference in smoking rates between males and females Signup and view all the answers

What is the correct conclusion if the p-value is less than the level of significance?

Reject the null hypothesis Signup and view all the answers

In the context of the diabetes treatment example, what does the alternative hypothesis (H1) state?

The mean reduction in blood glucose is different between groups Signup and view all the answers

Which of the following represents a Type II error?

Failing to reject a false null hypothesis Signup and view all the answers

What is one of the last steps in the hypothesis testing process?

Draw a conclusion from the test Signup and view all the answers

In the provided smoking rate example, what is the correct decision if H0 is true?

Conclude smoking rates are equal among genders Signup and view all the answers

What is a common significance level used in hypothesis testing?

0.05 Signup and view all the answers

Study Notes

Hypothesis Testing

A statement about the value of a population parameter is called a null hypothesis.
There are two types of hypotheses used in statistical testing: the null hypothesis (H0) and the alternative hypothesis (H1).
the null hypothesis is a statement of no effect or no difference, while the alternative hypothesis is a statement that there is an effect or a difference.
The null hypothesis is always tested against an alternative hypothesis, which is the opposite of the null hypothesis.
Hypothesis testing aims to determine if there is enough evidence to reject the null hypothesis.
The level of significance (α) is the probability of rejecting the null hypothesis when it is actually true.
Type I error occurs when the null hypothesis is true but is rejected. It is also referred to as a false positive.
Type II error occurs when the null hypothesis is false but is not rejected. It is also referred to as a false negative.
If the null hypothesis is false, the alternative hypothesis is accepted.
The rejection probability of the null hypothesis when it is true is called the level of significance (α).
A two-tailed test is used when the critical region is evenly distributed.
Type I error occurs when we reject a true null hypothesis. ### P-Value
The p-value is the probability of observing a result as extreme as the one obtained, assuming the null hypothesis is true.
A lower p-value indicates stronger evidence against the null hypothesis.
The p-value is compared to the significance level (α) to determine whether to reject the null hypothesis.
If the p-value is less than the significance level, the null hypothesis is rejected.
If the p-value is greater than the significance level, the null hypothesis is not rejected.

Summary of Steps for Hypothesis Testing

Step 1: Define the null and alternative hypotheses.
Step 2: Choose the level of significance (α).
Step 3: Choose the appropriate statistical test and compute the test statistic.
Step 4: Compute the p-value.
Step 5: Compare the p-value to the significance level (α) and determine whether to reject the null hypothesis.
Step 6: Draw a conclusion from the test based on whether the null hypothesis was rejected or not.

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Description

This quiz explores the fundamentals of hypothesis testing in statistics, including the definitions and roles of the null and alternative hypotheses. It also covers concepts like significance levels and types of errors that can occur during testing. Test your understanding of these key statistical principles!