Hypothesis testing confidence and significance

Question 1

What is a hypothesis in research?

Answer 1

A testable statement explaining beliefs about observed phenomena

Hypotheses can be formulated based on observations of trends or phenomena.

Question 2

What is the Null Hypothesis (H₀)?

Answer 2

There is no effect or difference

In an exercise example, H₀ would state that the population mean hours of exercise are zero.

Question 3

What is the Alternative Hypothesis (Hₐ)?

Answer 3

There is an effect or a difference

In an exercise example, Hₐ would suggest that the population mean hours of exercise are not zero.

Question 4

What happens if we reject the Null Hypothesis (H₀)?

Answer 4

We accept the Alternative Hypothesis (Hₐ)

Rejecting H₀ indicates that the sample data provides sufficient evidence against it.

Question 5

What is a Type I Error?

Answer 5

False positive; rejecting H₀ when it is true

Example: Concluding smoking affects lung cancer when it doesn’t.

Question 6

What is a Type II Error?

Answer 6

False negative; failing to reject H₀ when it is false

Example: Not detecting a relationship between smoking and lung cancer when one exists.

Question 7

What does the term ‘Power’ refer to in hypothesis testing?

Answer 7

The probability of correctly rejecting a false null hypothesis

Researchers typically aim for a power of 0.80.

Question 8

What factors affect the chances of committing Type I or Type II errors?

Answer 8

• Sample Size
• Effect Size

A larger sample size increases the chance of detecting a true effect.

Question 9

What is the purpose of Power Analysis?

Answer 9

To determine the necessary sample size or evaluate the statistical power of a test

Power Analysis can be conducted a-priori or a-posteriori.

Question 10

What are the two types of Power Analysis?

Answer 10

• A-Priori Power Analysis
• A-Posterior Power Analysis

A-Priori is done before the study, while A-Posterior is done after.

Question 11

What is the role of the p-value in hypothesis testing?

Answer 11

Quantifies the strength of evidence against H₀

If p-value ≤ 0.05, we reject H₀; otherwise, we fail to reject H₀.

Question 12

Fill in the blank: The Null Hypothesis (H₀) assumes _______.

Answer 12

[no effect or difference]

Question 13

Fill in the blank: The Alternative Hypothesis (Hₐ) suggests _______.

Answer 13

[there is an effect or a difference]

Question 14

In hypothesis testing, what does a sample mean falling in the rejection area indicate?

Answer 14

We reject the Null Hypothesis (H₀)

The rejection area is defined by the significance level (e.g., α = 0.05).

Question 15

What is the significance level commonly set at for hypothesis testing?

Answer 15

0.05 (5%)

This level determines the threshold for rejecting the null hypothesis.

Question 16

What is the purpose of formulating hypotheses in research?

Answer 16

To establish a basis for testing and making inferences about a population parameter

Hypotheses guide the research direction and statistical testing.

Question 17

What is the first step in hypothesis testing?

Answer 17

State the Hypotheses

This includes defining both the null and alternative hypotheses.

Question 18

What type of test is used to evaluate whether the population mean is equal to a specific value?

Answer 18

One-Sample t-Test

This test compares the sample mean against a known population mean.

Question 19

What does the sample standard deviation reflect in hypothesis testing?

Answer 19

The variability of the sample data

It is crucial for calculating the test statistic.

Question 20

What is a common method used to perform hypothesis testing in statistical software?

Answer 20

SPSS

SPSS provides various statistical tests, including t-tests and chi-square tests.

Question 21

What is the significance of the degrees of freedom (df) in hypothesis testing?

Answer 21

It affects the shape of the t-distribution used in tests

Degrees of freedom are typically calculated based on sample size.

Question 22

What does SPSS provide for descriptive statistics?

Answer 22

Mean, standard deviation, standard error

These statistics help summarize the central tendency and variability of data.

Question 23

What is the test statistic (t) in the given SPSS output?

Answer 23

-24.106

This value indicates the calculated t-value for the hypothesis test.

Question 24

What is the degrees of freedom (df) in the SPSS output?

Answer 24

99

Degrees of freedom are a parameter used in various statistical tests.

Question 25

What conclusion can be drawn if the p-value is <0.001?

Answer 25

Reject H₀

This indicates that the result is statistically significant.

Question 26

What is the null hypothesis (H₀) in the one-sample chi-square test example?

Answer 26

π = 0.5

This hypothesis states that the observed proportion equals the hypothesized proportion.

Question 27

What is the alternative hypothesis (Hₐ) in the one-sample chi-square test example?

Answer 27

π ≠ 0.5

This hypothesis states that the observed proportion is different from the hypothesized proportion.

Question 28

What is the test statistic (χ²) in the one-sample chi-square SPSS output?

Answer 28

40.091

This value reflects the calculated chi-square statistic for the hypothesis test.

Question 29

What is the p-value in the one-sample chi-square SPSS output?

Answer 29

<0.001

A p-value this low indicates strong evidence against the null hypothesis.

Question 30

What conclusion can be drawn if p < 0.05 in the chi-square test?

Answer 30

Reject H₀

This indicates that the observed proportion is significantly different from 50%.

Question 31

What are the structured steps in hypothesis testing in SPSS?

Answer 31

Formulating hypotheses, testing with sample data, interpreting p-values

These steps guide the analysis of scientific data.

Question 32

What is the significance of understanding statistical tests like the t-test and chi-square test?

Answer 32

Helps draw meaningful conclusions in various fields

Knowledge of these tests is essential for data analysis.