Psychological Statistics Midterm Module 2

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Questions and Answers

What is the primary purpose of hypothesis testing?

To identify all variables without making predictions.

To establish a definitive conclusion about a population.

To evaluate a hypothesis using sample data. (correct)

To predict outcomes based on historical data.

Which step is NOT part of the four steps of a hypothesis test?

Make a decision

Collect data and compute results

Conduct a literature review (correct)

State the hypothesis

What does a Type I error indicate in hypothesis testing?

Rejecting a null hypothesis that is false.

Accepting a null hypothesis that is true.

Failing to reject a false null hypothesis.

Rejecting a null hypothesis that is true. (correct)

Which of the following best defines the alpha level in hypothesis testing?

The threshold for determining statistical significance. Signup and view all the answers

When calculating the z-score for a sample mean, which values are essential?

Sample size and population standard deviation. Signup and view all the answers

What is a Type II error in hypothesis testing?

Failing to detect an effect that is present. Signup and view all the answers

In hypothesis testing, what is meant by the critical region?

The extreme sample values that are very unlikely under the null hypothesis. Signup and view all the answers

What is primarily focused on in a hypothesis test?

The data collected Signup and view all the answers

Which factor can increase the power of a statistical test?

Increasing the sample size Signup and view all the answers

What must be determined to evaluate a hypothesis using sample data?

The relationship between two or more variables. Signup and view all the answers

What does a significant treatment effect not necessarily imply?

That the treatment effect is substantial Signup and view all the answers

What relationship does the alpha level have with the power of a test?

Increasing alpha increases power Signup and view all the answers

Which measure is used to estimate the real standard error when the value of σ is unknown?

Estimated Standard Error (sM) Signup and view all the answers

Which of the following statements is true regarding one-tailed and two-tailed tests?

One-tailed tests predict the direction of the treatment effect Signup and view all the answers

What does the degrees of freedom represent in a sample?

The number of scores that are independent and can vary Signup and view all the answers

What does measuring effect size provide insight into?

The strength or magnitude of a treatment effect Signup and view all the answers

What does a Type II error indicate in hypothesis testing?

A treatment effect is not detected when it does exist. Signup and view all the answers

Which factor is NOT considered when determining the boundaries of the critical region?

Sample size Signup and view all the answers

What happens to the standard deviation when a constant is added or subtracted from a dataset?

It is unaffected by the addition or subtraction of a constant. Signup and view all the answers

What is represented by the symbol β (beta) in hypothesis testing?

The probability of a Type II error Signup and view all the answers

What does a significant result in a statistical test imply about the null hypothesis?

It has been rejected. Signup and view all the answers

Which of the following is a characteristic of independent observations?

Each event outcome has no impact on the probability of the next. Signup and view all the answers

Which of the following best describes a one-tailed hypothesis test?

It specifies either an increase or a decrease in the population mean. Signup and view all the answers

What does a Type I error represent in hypothesis testing?

The null hypothesis is rejected when it is true. Signup and view all the answers

Which of the following assumptions is crucial for conducting hypothesis tests with z-scores?

The sample data must have a normal distribution. Signup and view all the answers

How does higher variability of scores influence a hypothesis test's outcome?

It decreases the z-score value. Signup and view all the answers

In hypothesis testing, what does it mean if sample data fall within the critical region?

The null hypothesis is rejected. Signup and view all the answers

What is the purpose of measuring effect size in hypothesis testing?

To measure the absolute magnitude of a treatment effect. Signup and view all the answers

Which factor would lead to a larger value for the z-score in hypothesis testing?

Increasing the number of scores in the sample. Signup and view all the answers

According to Cohen's criteria, how can effect size be standardized?

By measuring mean differences in terms of the standard deviation. Signup and view all the answers

In hypothesis testing, what does it mean if a result is said to be statistically significant?

The null hypothesis is unlikely to be true. Signup and view all the answers

What may cause a decrease in the chance of finding a significant treatment effect?

Lower sample size. Signup and view all the answers

What does the term 'effect size' refer to in the context of treatment variability?

A measurement that quantifies the impact of treatment on variability. Signup and view all the answers

What is the purpose of calculating a confidence interval?

To estimate the population parameter from a sample statistic. Signup and view all the answers

Which of the following correctly states the null hypothesis in a one-tailed t-test with the alternative hypothesis suggesting a decrease?

Ho: μ ≥ 0, H1: μ < 0 Signup and view all the answers

How is the critical value for a two-tailed test determined?

It utilizes the degrees of freedom and alpha level. Signup and view all the answers

In a t-test with 9 samples, what is the appropriate degree of freedom (df) to use?

8 Signup and view all the answers

What is the critical value of t for a one-tailed test at α = 0.01 with 8 degrees of freedom?

2.896 Signup and view all the answers

What does the term 'critical region' refer to in hypothesis testing?

The range of values in which we reject the null hypothesis. Signup and view all the answers

Which statement about hypothesis testing is false?

Rejecting the null hypothesis guarantees that it is false. Signup and view all the answers

Study Notes

Statistical Inference and Hypothesis Testing

Every sample mean (M) has a z-score indicating its position within the distribution of sample means.
Hypothesis: Predicts the relationship between variables; serves as a scientific guess.
A hypothesis test evaluates a hypothesis about a population using sample data.
Hypothesis testing employs statistical analysis to address research questions.

Steps in Hypothesis Testing

Step 1: State the hypothesis.
Step 2: Set criteria for making decisions based on data.
Step 3: Collect data and compute sample statistics.
Step 4: Make a decision regarding the null hypothesis.

Types of Errors in Hypothesis Testing

Type I Error (False Positive): Rejecting a true null hypothesis, indicating treatment effect where none exists.
Type II Error (False Negative): Failing to reject a false null hypothesis, missing a real treatment effect.
Critical region determined by alpha level, which defines extreme sample values unlikely if the null hypothesis is true.

Z-Scores

Z-score for Population: Reflects an individual score's position in the entire score distribution.
Z-score for Sample: Reflects a sample mean's position within the distribution of sample means.

Assumptions for z-Score Hypothesis Tests

Random Sampling: Ensures sample is representative of the population.
Independent Observations: The occurrence of one event does not affect another.
Value of σ remains unchanged by treatment, affecting only the mean, not standard deviation.

Reporting Results in Statistical Tests

A significant result indicates the null hypothesis is rejected, unlikely to occur by chance alone.
Directional (One-Tailed) Hypothesis Tests specify expected direction of effect (increase/decrease).

Measuring Effect Size

Effect size quantifies the magnitude of a treatment effect, independent of sample size.
Cohen (1988) suggested standardizing effect size by measuring mean difference relative to standard deviation.

Factors Influencing Hypothesis Test Outcomes

Score Variability: Higher variability may decrease likelihood of significant results due to reduced z-score value.
Sample Size: Larger samples provide smaller standard errors and larger z-scores, increasing power.
Alpha Level: Lowering alpha level reduces test power but decreases Type I error risk.

Power of a Statistical Test

Probability of correctly rejecting a false null hypothesis increases with larger sample sizes.
Parametric tests generally have greater power than non-parametric counterparts.
Power calculations help determine if the sample size is sufficient.

t-Statistic in Hypothesis Testing

Used when population parameters are unknown, forms the basis of t-tests.
Critical region locations depend on the degrees of freedom (df) determined by sample size.

Confidence Intervals

Represent a range of values around a sample statistic, predicting the population parameter.
Confidence intervals provide insight into where the true population parameter likely falls.

Hypotheses must clearly define expected differences between conditions (e.g., swearing and pain tolerance).
Specify the alpha level to determine critical values for decision-making in hypothesis testing.

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Description

This quiz covers key concepts from Module 2 of Psychological Statistics, focusing on hypothesis testing, effect size, and types of errors. It explores the relationship between sample means and z-scores, providing a comprehensive assessment of your understanding of statistical inference.