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Questions and Answers
What is the null hypothesis in the study comparing resting pulse rates between exercisers and non-exercisers?
What is the null hypothesis in the study comparing resting pulse rates between exercisers and non-exercisers?
Which statistical test was used to compare the resting pulse rates of adult subjects in the study?
Which statistical test was used to compare the resting pulse rates of adult subjects in the study?
What conclusion is drawn if the p-value is less than the significance level α?
What conclusion is drawn if the p-value is less than the significance level α?
What conditions must be verified before performing a t-test in this study?
What conditions must be verified before performing a t-test in this study?
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Based on the study's results, what was the conclusion regarding the mean resting pulse rates?
Based on the study's results, what was the conclusion regarding the mean resting pulse rates?
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What is the significance level (α) used in the study?
What is the significance level (α) used in the study?
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If the t-test statistic is larger than the t critical value, what does this indicate?
If the t-test statistic is larger than the t critical value, what does this indicate?
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How many subjects were in the non-exercisers' group?
How many subjects were in the non-exercisers' group?
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What are the degrees of freedom used for the t-test in this study?
What are the degrees of freedom used for the t-test in this study?
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What would be the p-value if it is stated that p-value < 0.001?
What would be the p-value if it is stated that p-value < 0.001?
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What is the correct null hypothesis for a two-sided test comparing two means?
What is the correct null hypothesis for a two-sided test comparing two means?
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What must be verified in Step 2a of the significance test process?
What must be verified in Step 2a of the significance test process?
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For a two independent sample t-test, how is the test statistic calculated?
For a two independent sample t-test, how is the test statistic calculated?
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When is a large random sample required when the population is not approximately normal?
When is a large random sample required when the population is not approximately normal?
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What determines the degrees of freedom for the t-test statistic in a two independent sample t-test?
What determines the degrees of freedom for the t-test statistic in a two independent sample t-test?
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What is the range of the p-value if the t-statistic is -2.50 for a one-sided test with df = 9?
What is the range of the p-value if the t-statistic is -2.50 for a one-sided test with df = 9?
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What action should be taken if the p-value is less than or equal to the chosen level of significance α?
What action should be taken if the p-value is less than or equal to the chosen level of significance α?
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In a two-sided test, what conclusions can be drawn if the p-value is between 0.02 and 0.04?
In a two-sided test, what conclusions can be drawn if the p-value is between 0.02 and 0.04?
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What is the main purpose of conducting a significance test?
What is the main purpose of conducting a significance test?
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What does a t-statistic of -2.50 indicate in a two independent sample t-test?
What does a t-statistic of -2.50 indicate in a two independent sample t-test?
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Study Notes
Two Independent Sample t-Test
- Purpose: A statistical test used to compare the means of two independent groups.
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Conditions:
- Normally Distributed Populations: Both populations must be approximately normally distributed, OR large sample sizes (n1 + n2 ≥ 40) are required.
- Random Samples: Both samples must be randomly selected from their respective populations.
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Hypotheses:
- Null Hypothesis (H0): There is no difference between the population means.
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Alternative Hypothesis (Ha): There is a difference between the population means.
- Two-Sided: The difference is not specified (µ1 ≠ µ2)
- One-Sided: The difference is specified in a specific direction (µ1 < µ2 or µ1 > µ2)
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Test Statistic: Measures how far apart the sample means are from each other, relative to the variability within each group.
- Follows the t-distribution with degrees of freedom determined by the smaller sample size minus 1.
- Formula: t = (sample mean difference - hypothesized difference) / standard error of the difference
- P-Value: The probability of obtaining sample results as extreme as observed, assuming the null hypothesis is true.
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Decision & Conclusion:
- Reject the Null Hypothesis: If the P-value is less than or equal to the significance level (α), reject the null and conclude there is significant evidence for the alternative.
- Fail to Reject the Null Hypothesis: If the P-value is greater than α, fail to reject the null and conclude there is not enough evidence to support the alternative hypothesis.
Exercise and Pulse Rates Example
- Study Objective: Investigate the potential difference in mean resting pulse rates between adults who regularly exercise and those who do not.
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Sample Data:
- Non-Exercisers: n = 31, mean = 75, standard deviation = 9.0
- Exercisers: n = 29, mean = 66, standard deviation = 8.6
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Hypotheses:
- H0: The mean resting pulse rate of non-exercisers is equal to the mean resting pulse rate of exercisers.
- Ha: The mean resting pulse rate of non-exercisers is different from the mean resting pulse rate of exercisers.
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Test Results:
- T-statistic: Large enough to reject the null hypothesis based on the t-distribution with 28 degrees of freedom.
- P-value: Less than 0.001 (two-sided).
- Conclusion: There is strong evidence to conclude that the mean resting pulse rate of adults who do not exercise regularly is significantly different from the mean resting pulse rate of those who do exercise regularly.
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Description
This quiz covers the essential aspects of the Two Independent Sample t-Test, including conditions, hypotheses, and test statistics. It provides a foundational understanding necessary for comparing the means of two independent groups in statistics. Ideal for students looking to deepen their statistical analysis skills.
