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1 2 4 TMEREMANING David wants to complete a hypothesis test with the least amount of probability for error. If he sets the significance level to \( 1 \% \), assuming his sample is truly random, what else could he adjust in the test in order to reduce error? He could change the population mean. He could increase the sample size. He could change the population standard deviation. He could decrease the sample size.

Ask by Pearson Frank. in the United States
Feb 25,2025

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Answer

To reduce error in the hypothesis test, David should increase the sample size.

Solution

The best option is to increase the sample size. Increasing the sample size reduces the standard error, which makes it easier to detect true effects while lowering the chance of making type II errors (failing to reject a false null hypothesis). This adjustment enhances the overall power of the test without affecting the type I error rate, which, in this scenario, is already set at 1%.

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Bonus Knowledge

Increasing the sample size is a powerful strategy David can use to reduce the error rate in his hypothesis test. A larger sample size leads to a more accurate estimate of the population parameters and reduces the standard error, making it easier to detect true effects. Statistically, this means that with a larger sample, the probability of committing Type I and Type II errors decreases, allowing for more reliable conclusions. Another effective way to bolster his results is by improving the data collection process to ensure that the samples are representative of the population. This means avoiding sampling biases and ensuring a truly random selection. By addressing these methodological aspects, he can strengthen the validity of his test findings.

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