Problemas
Scenario 2: Statisticians prefer larger sample sizes to smaller sample sizes, Assuming the mean and standard deviation of all samples remain constant, what are the effects of increasing the number of participants in a study from 10 to 50? The standard error of the test would:Select] square The margin of error of a 95% confidence interval would: square The t-statistic for the test would: [Select] square The critical value for the test would:Select | square
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When increasing the number of participants in a study from 10 to 50, assuming the mean and standard deviation remain constant, the following effects occur:1. **Standard Error of the Test:** - The standard error of the test would **decrease**. - Explanation: The standard error is calculated as the standard deviation divided by the square root of the sample size (\( \text{SE} = \frac{\sigma}{\sqrt{n)). sample size increases, the denominator increases, leading to a smaller standard error.2. **Margin of Error of a 95% Confidence Interval:** - The margin of error of a 95% confidence interval would **decrease**. - Explanation: The margin of error is directly related to the standard error. Since the standard error decreases with an increase in sample size, the margin of error also decreases.3. **t-Statistic for the Test:** - The t-statistic for the test would **not change**. - Explanation: The t-statistic is calculated based on the sample mean, sample standard deviation, and sample size. Since the mean and standard deviation remain constant, the t-statistic does not change with an increase in sample size.4. Value for** - The critical value for the test would **not change**. - Explanation: The critical value is determined by the desired level of confidence and the degrees of freedom, which are related to the sample size. However, for a of confidence (e.g., 95%), the critical value remains the same regardless of the sample size.In summary:- The standard error of the test would decrease.- The margin of error of a 95% confidence interval would decrease.- The t-statistic for the test would not change.- The critical value for the test would not change.