Biostatistics- WA 5

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University of the People *

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CPH 4510

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Health Science

Date

Jan 9, 2024

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docx

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7

Uploaded by SuperKuduMaster89

1 Sampling and Hypothesis Testing Sampling and Hypothesis Testing Department of Health Science, University of The People HS 4510 – 01 Biostatistics Adaugo Eziyi December 20 th , 2023
2 Sampling and Hypothesis Testing Sampling and Hypothesis Testing 1. A consumer group suspects that a soft drink has higher sugar levels than what is acceptable. They hire a researcher to investigate this issue. Write a null and alternative hypothesis for this study. Null Hypothesis ( H 0 ): The soft drink has sugar levels that are within the acceptable range. Alternative Hypothesis ( H 1 ): The Soft drink has higher sugar levels than what is acceptable. Explain in words what a Type 1 error would mean in this situation. A type 1 error is made “when we reject the null hypothesis when it is actually true” (University of The People, 2023) In this situation, a type 1 error would mean that the soft drink has higher sugar levels than what is acceptable, even though it does not. Explain in words what a Type 2 error would mean in this situation. Type 2 error is made “when we accept the null hypothesis when it is false” (University of The People, 2023). In this situation, a type 2 error would mean failing to conclude that the soft drink has higher sugar levels than what is acceptable, even though it does. 2. In a research study, you decided to change the significance level from the standard 0.05 to 0.01. Explain how this would influence:
3 Sampling and Hypothesis Testing Type 1 error Type 1 Error: The significance level also known as alpha, “is the probability of rejecting the null hypothesis when it is true” (Minitab, 2015). By decreasing the level of significance from 0.05 to 0.01, you are making it stricter. This means that the probability of committing a type 1 error which is rejecting the null hypothesis when it is actually true, decreases— meaning, you become more conservative in claiming statistical significance. Type 2 error Type 2 Error: Type 2 error occurs when we accept the null hypothesis when it is false. Decreasing the level of significance from 0.05 to 0.01 does not directly affect the type 2 error rate. However, as the level of significance decreases and become stricter, the chances of committing a type 2 error tends to increase. This is because you are setting a higher bar for rejecting the null hypothesis making it harder to detect a true effect if it is present. Power Power: Power is the probability of “rejecting the null hypothesis when it is false” (University of The People, 2023). By decreasing the level of significance, you are decreasing the probability of rejecting the null hypothesis, both for when it is true (type 1 error) and when it is false (type 2 error). As a result, this reduction in the probability of rejecting the null hypothesis decreases the statistical power of your study. Lower power means a lower ability to detect true effects, which can increase the chances of false negatives.
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