Two-tailed Test: Rejecting the Null at 0.05 Level of Significance

In summary, the conversation discusses a two-tailed test with a test statistic value of 2 and a Student's t-distribution with a probability of T>2 = 0.03. It is determined that there is not enough evidence to reject the null hypothesis at a significance level of 0.05 due to the two-tailed nature of the test. The individual seeking help initially thought the answer was "True" but then realized they were overthinking the problem.
  • #1
elove
17
0
In a two-tailed test, the value of the test statistic is 2. If we know the test statistic follows a Student’s t- distribution with P
(T>2) = 0.03, then we have sufficient evidence to reject the null hypothesis at 0.05 level of significance.

I want to say True but I think I'm overthinking the problem. Can anyone help me out?
 
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  • #2
The problem is, it's a two-tailed test. If you take $0.05$ as your significance level, then you'd need $0.025$ probability in each tail. But your $P$ value is $0.03>0.025$. Therefore, you do not have sufficient statistical evidence to reject the null hypothesis.
 
  • #3
Yes! I get tripped up working backwards on problems. two-tailed - 0.05/2 = 0.025. I understand - thank you! I feel silly now on such a simple problem.
 

FAQ: Two-tailed Test: Rejecting the Null at 0.05 Level of Significance

What is a two-tailed test?

A two-tailed test is a statistical test used to determine if the observed data is significantly different from the expected data. In this test, the null hypothesis is rejected if the observed data falls in either tail of the distribution, indicating a significant difference.

What does it mean to reject the null hypothesis at 0.05 level of significance?

Rejecting the null hypothesis at 0.05 level of significance means that there is a 5% chance that the observed data is due to random chance. This is the commonly accepted threshold for determining if the results are statistically significant.

How is the 0.05 level of significance chosen?

The 0.05 level of significance is chosen to balance the risk of making a Type I error (incorrectly rejecting the null hypothesis) and a Type II error (incorrectly failing to reject the null hypothesis). It is a commonly used threshold in scientific research, but it can vary depending on the field of study and the specific research question.

Can a two-tailed test be used for any type of data?

Yes, a two-tailed test can be used for any type of data as long as it follows a normal distribution. This type of test is commonly used in hypothesis testing for quantitative data, such as means or proportions.

What are the advantages of using a two-tailed test?

One advantage of using a two-tailed test is that it allows for a more comprehensive analysis of the data, as it considers both sides of the distribution. This can provide more accurate and reliable results. Additionally, a two-tailed test can be used to test for both positive and negative effects, making it more versatile compared to a one-tailed test.

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