If a researcher computes ten (10) t-tests for comparing five means at the 0.05 significance level, then:
A. The overall Type II Error rate for the experiment will increase.
B. The probability is 0.50 to reject at least one null hypothesis, when it is true.
C. There will be an unacceptable high error rate for the total experiment.
D. The overall Type I Error rate for the experiment will increase.
E. The rate of Type I and II errors for the experiment will remain equal.
Choose the correct answer from the options given below:

Correct option is C

The correct answer is (c) "B, C and D only."
Explanation: When a researcher computes multiple t-tests at the 0.05 significance level, the overall Type I error rate (the probability of incorrectly rejecting a true null hypothesis) increases, leading to an unacceptably high error rate for the total experiment. Specifically, with 10 t-tests, the probability of making at least one Type I error across the tests becomes significant. This increase in error rate is a known issue when conducting multiple comparisons without adjustments, such as the Bonferroni correction.
Information Booster:
1. Type I Error: Occurs when a true null hypothesis is incorrectly rejected. The probability of committing this error increases with the number of comparisons.
2. Type II Error: Involves failing to reject a false null hypothesis. While the focus in this question is on Type I error, Type II error is also a critical consideration in hypothesis testing.
3. Multiple Comparisons Problem: Conducting multiple statistical tests increases the risk of Type I errors. Researchers often adjust significance levels or use corrections to mitigate this risk.
4. Bonferroni Correction: A method used to counteract the problem of multiple comparisons by adjusting the significance level.
5. Experiment-Wise Error Rate: The overall probability of making one or more Type I errors across all the tests conducted in an experiment.
6. Significance Level (Alpha): Typically set at 0.05, it represents the threshold for rejecting the null hypothesis. Multiple tests without correction inflate the overall error rate.
Additional Information:
· Type II Error: Although important, the overall Type II error rate is not directly addressed in the context of multiple t-tests in this scenario.
· Significance Levels: Researchers must be cautious when interpreting results from multiple tests, ensuring that the increased risk of Type I errors is accounted for in their analysis.
Key Points:
· Conducting multiple t-tests increases the overall Type I error rate, leading to a higher likelihood of incorrect rejections.
· Proper statistical adjustments are necessary to maintain the integrity of experimental results.
· Understanding the impact of multiple comparisons is crucial for accurate hypothesis testing in research.