Multiple Choice. If a Runs Test for Randomness is conducted at the a = 0.05 leve
ID: 3227541 • Letter: M
Question
Multiple Choice. If a Runs Test for Randomness is conducted at the a = 0.05 level of significance, with the outcome counts n_1 = 11 and n_2 = 13, what is the lowest number of observed runs G_cac, that will NOT result in rejection of the null hypothesis? a. 6 b. 7 c. 8 d. 19 e. 20 f. 21 State whether each of the following hypothesis tests can be one-tailed only, two-tailed, or either one-tailed or two-tailed. a. The Sign Test For Matched b. The Test for Spearman's Rank Correlation c. The Test For Pearson's Linear Correlation d. The Runt Test For RandomnessExplanation / Answer
Answer to question 9)
if the value of Gc&c lies between the critical values of runs, we do not reject the null hypothesis
Since we are looking for the least value that leads to rejection, it would be somthing that is above the upper critical value
We get to know the critical values from the run table for alpha = 0.05
n1 = 11 and n2 = 13
We get the critical values as : (7 & 19)
Thus the rejection values would be : r < 7 and r > 19
So the least value for which rejection happens from the given options is r=20
Thus the correct answer choice is e) r=20
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Answer to question# 10)
a) the sign test for matched pairs can be either one tailed or two tailed
If the hypothesis states that the median > 0 , then it becomes one tailed
If the hypothesis states that the median 0 , then the test is considered to be two tailed
We get critical values for both the types of tests.
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b) The Test for Spearman's Rank Correlation:
The rank correlation test is to find if there is significant correlation between the two variables or not
In that case the focus is on find if r 0 , in that case the only possibility for the test is to be a "two tailed test"
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c) The Test for Pearson's Linear Correlation
Again , since this test is about th identification of the linear correlation it is by default a Two tailed test
.
d) The run tests for randomness:
This test can be a one tailed or a two tailed test base don the hypothesis so designed
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