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Questions and Answers
What is the function of the null hypothesis in a hypothesis test?
What is the function of the null hypothesis in a hypothesis test?
What is the interpretation of a 95% confidence interval for the population mean?
What is the interpretation of a 95% confidence interval for the population mean?
What is the purpose of a paired samples t-test?
What is the purpose of a paired samples t-test?
What is the definition of a p-value?
What is the definition of a p-value?
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What is the difference between a one-sample t-test and an independent samples t-test?
What is the difference between a one-sample t-test and an independent samples t-test?
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What is the purpose of specifying a direction in an alternative hypothesis?
What is the purpose of specifying a direction in an alternative hypothesis?
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Study Notes
Hypothesis Testing
Null and Alternative Hypotheses
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Null Hypothesis (H0): A statement of no effect or no difference.
- Example: There is no significant difference in the average score of students who received additional tutoring and those who did not.
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Alternative Hypothesis (H1): A statement of an effect or difference.
- Example: There is a significant difference in the average score of students who received additional tutoring and those who did not.
- Direction of the Alternative Hypothesis: One-tailed (directional) or two-tailed (non-directional)
Confidence Intervals
- Definition: A range of values within which the true population parameter is likely to lie.
- Interpretation: A (1 - α)100% confidence interval for a population parameter is an interval that has a (1 - α) probability of containing the true population parameter.
- Example: A 95% confidence interval for the population mean is (10, 15). This means that there is a 95% probability that the true population mean lies between 10 and 15.
T-tests
- Independent Samples T-test: Compares the means of two independent groups.
- Paired Samples T-test: Compares the means of two related groups (e.g., before and after treatment).
- One Sample T-test: Compares the mean of one group to a known population mean.
P-values
- Definition: The probability of obtaining a result as extreme or more extreme than the one observed, assuming that the null hypothesis is true.
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Interpretation:
- If p-value ≤ α (significance level), reject the null hypothesis.
- If p-value > α, fail to reject the null hypothesis.
- Example: If the p-value is 0.01 and α = 0.05, reject the null hypothesis because 0.01 ≤ 0.05.
Normal Distribution
- Definition: A continuous probability distribution with a symmetrical bell-shaped curve.
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Properties:
- Mean (μ) = Median = Mode
- Symmetrical around the mean
- Bell-shaped curve
- Importance in Hypothesis Testing: Many statistical tests assume normality of the data or the sampling distribution of the test statistic.
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Description
Understand the basics of hypothesis testing, including null and alternative hypotheses, confidence intervals, t-tests, p-values, and the importance of normal distribution in statistical testing.
