Hypothesis Testing

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Questions and Answers

What is the primary goal of a researcher when analyzing a sample?

To eliminate all random variability

To prove a specific hypothesis

To compute the exact statistics for the sample

To generalize findings to a larger population (correct)

What term is used to describe the corresponding values of a population?

Means

Sample values

Parameters (correct)

Statistics

What does sampling error refer to?

A systematic issue in data collection

An error in the methodology used

The variation in statistics from one sample to another (correct)

The mistakes made during sample selection

What primarily causes Type II errors in research design?

The sample size is too small. Signup and view all the answers

If a sample shows a statistical relationship, what can be concluded about the population?

The relationship in the population is uncertain and may be due to sampling error Signup and view all the answers

How can the chance of a Type I error be reduced?

By setting α to less than 0.05. Signup and view all the answers

What implication does the presence of random variability have on statistical conclusions?

It introduces uncertainty in interpreting population parameters Signup and view all the answers

Why might the mean number of depressive symptoms differ across various samples?

Because of random variability in sample statistics Signup and view all the answers

What is the implication of lowering αlpha to reduce Type I errors?

Increases the chance of Type II errors. Signup and view all the answers

What is the relationship between sample statistics and population parameters?

Sample statistics can be used to approximate population parameters Signup and view all the answers

Why do researchers consider replicating studies important?

To check for Type I or Type II errors. Signup and view all the answers

What is the commonly accepted significance level among researchers to manage errors?

0.05 Signup and view all the answers

What is the purpose of null hypothesis testing?

To decide between two interpretations of a statistical relationship in a sample Signup and view all the answers

What does the null hypothesis (H0) represent?

There is no relationship in the population Signup and view all the answers

What is the significance level often set to in null hypothesis testing?

.05 Signup and view all the answers

What happens if the p value is lower than your alpha level?

The null hypothesis is rejected Signup and view all the answers

What is a Type I error?

Rejecting the null hypothesis when it is true Signup and view all the answers

When is a result considered statistically significant?

When the p value is smaller than or equal to .05 Signup and view all the answers

What does a Type II error signify?

Concluding there is no relationship when there is one Signup and view all the answers

What is the logical first step in null hypothesis testing?

Assume the null hypothesis is true Signup and view all the answers

What questions did Mehl and his colleagues investigate regarding talkativeness? (refer to reading)

Is there a sex difference in talkativeness? Signup and view all the answers

If a researcher states 'fail to reject the null hypothesis', what does it indicate?

Insufficient evidence to reject the null hypothesis Signup and view all the answers

Study Notes

Null Hypothesis Testing

Researchers aim to draw conclusions about populations based on samples.
Sample statistics are estimates of population parameters.
Sampling error refers to random variability in a statistic from sample to sample.
Statistical relationships in a sample may or may not reflect population relationships.
The null hypothesis (H₀) posits no relationship in the population.
The alternative hypothesis (H₁) posits a relationship in the population.

Logic of Null Hypothesis Testing

Assume the null hypothesis is true.
Assess the likelihood of the sample relationship if H₀ were true.
Reject H₀ if the sample relationship is highly unlikely.
Retain H₀ if the sample relationship is not highly unlikely.
p-value represents the likelihood of the sample result under H₀.
A low p-value suggests the sample result is unlikely under H₀, leading to rejection.
α (alpha) is the criterion for rejecting H₀, usually set to 0.05.
A statistically significant result has a p-value ≤ α.

Type I and Type II Errors

Type I error: Rejecting H₀ when it's true. This means concluding there's a relationship when none exists.
- Occurs due to sampling error.
- Probability of Type I error is α.
Type II error: Retaining H₀ when it's false. This means concluding there's no relationship when one does exist.
- Often due to low statistical power (insufficient sample size).
Researchers must balance the risk of both types of errors.
Lowering the risk of one type increases the risk of another.
α=0.05 is a common compromise.
Replication is crucial to increase confidence in results.

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Description

This quiz covers the fundamentals of null hypothesis testing, including the definitions of null and alternative hypotheses, sampling error, and the logic behind hypothesis testing. Understand how sample statistics relate to population parameters and learn about p-values and significance levels.