18) Which of the following is the most significant result?
A) P<.001
B) P<.005
C) P=.05
D) P>.05
Okay, I have the answer key and know the question is A, but I always thought that if the P value is greater than .05 than it IS considered significant and you can reject your null hypothesis-am I wrong??
19) Also somewhat of a smilar question:
Which of the following is the most significant result?
A) t9df=2.538 for a 1-sided t- test
B) t15df=2.538 for a 2 sided t-test
C) t26df= 2.538 for a 1-sided t- test
D) t49df= 2.538 for a 2 sided t-test
I have the same problem here, the first multiple choice letter that I rejected (choice C) was the right answer?!?!
You can reject Ho if p ≤ .05, which means that the results you have found would happen by chance 5% of the time or less. P > .05 means that there is a greater than 5% probability that the results were due to chance. Under those conditions, I would not reject the Ho.
Since I have not worked in the area for some time, for your last question, I searched Google under the key words "t-test significance one-tailed 'degrees of freedom'" to get these possible sources:
http://www.psychstat.missouristate.edu/introbook/sbk25.htm
http://www.bized.co.uk/timeweb/crunching/crunch_experiment_reviewb.htm
http://books.google.com/books?id=2oEQyOIyCbUC&pg=RA1139-PA2&lpg=RA1139-PA2&dq=%22t+test%22+significance+%22one+tailed%22+%22degrees+of+freedom%22&source=web&ots=hJ038C041Z&sig=KfJKzwtnGcQEtpchFKHTdV13Mio&hl=en
http://www.bized.co.uk/timeweb/crunching/crunch_experiment_reviewb.htm
http://books.google.com/books?id=2oEQyOIyCbUC&pg=RA1139-PA2&lpg=RA1139-PA2&dq=%22t+test%22+significance+%22one+tailed%22+%22degrees+of+freedom%22&source=web&ots=hJ038C041Z&sig=KfJKzwtnGcQEtpchFKHTdV13Mio&hl=en
In the future, you can find the information you desire more quickly, if you use appropriate key words to do your own search.
I hope this helps. Thanks for asking.
Question 18:
The most significant result is A) P<.001.
In statistical hypothesis testing, the significance level (usually denoted as alpha, α) is the threshold at which the null hypothesis is rejected or not rejected. It represents the probability of observing a test statistic as extreme as the one computed from the sample if the null hypothesis is true.
A P-value is a measure of the evidence against the null hypothesis. It represents the probability of observing the data or more extreme data if the null hypothesis is true. The smaller the P-value, the stronger the evidence against the null hypothesis.
In this case, a P<.001 means that there is less than a 0.1% chance of observing the data or more extreme data if the null hypothesis is true. This is considered a highly significant result, indicating strong evidence against the null hypothesis.
Question 19:
The most significant result is C) t26df= 2.538 for a 1-sided t-test.
In this question, the degree of freedom (df) represents the number of independent observations available to estimate a parameter. A lower degree of freedom indicates a smaller sample size.
A t-value is a test statistic calculated from sample data in a t-test. It measures the difference between the sample mean and the null hypothesis mean in terms of standard error.
In this case, a t-value of 2.538 indicates the magnitude of the difference between the sample mean and the null hypothesis mean. The most significant result is the one with the lowest degree of freedom for a 1-sided t-test. Therefore, choice C is the correct answer.
18) In hypothesis testing, the p-value represents the probability of observing a test statistic as extreme as the one calculated or more extreme under the null hypothesis. The p-value is compared to the significance level (often denoted as α) to make a decision about rejecting or failing to reject the null hypothesis.
Typically, a significance level of α = 0.05 (or 5%) is commonly used. If the p-value is less than the significance level (p < α), then we have enough evidence to reject the null hypothesis in favor of the alternative hypothesis. This means that the result is statistically significant.
So, for question 18, the most significant result is option A) P<.001 because it has the smallest p-value. This indicates that there is an extremely low probability of observing the test statistic or more extreme under the null hypothesis.
You are correct that if the p-value is greater than the significance level (p > α), we would fail to reject the null hypothesis. However, the question asks for the "most significant" result, and in general, smaller p-values are considered more significant as they provide stronger evidence against the null hypothesis.
19) In this question, the t-value and degrees of freedom (df) are given for different t-tests. The same principle applies here as well. In a t-test, if the t-value is larger and/or the degrees of freedom are smaller, it indicates stronger evidence against the null hypothesis and therefore a more significant result.
Based on the given information, the most significant result would be option C) t26df=2.538 for a 1-sided t-test. The combination of a larger t-value and a relatively lower degree of freedom makes this result more significant compared to the others.
It's important to note that significance is not solely determined by the t-value. Degrees of freedom and the chosen alpha level also play a role in determining significance.
So, in both questions, the most significant results are those with smaller p-values or larger t-values with lower degrees of freedom, providing stronger evidence against the null hypothesis.