For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

The result is significant at both α = 0.05 and α = 0.01.
The result is significant at α = 0.05 but not at α = 0.01.
The result is significant at α = 0.01 but not at α = 0.05.
The result is not significant at either α = 0.05 or α = 0.01.
The result is inconclusive because we don't know the value of p.

Question

04-08-2017
Mathematics

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For a hypothesis test of H0:p1 − p2 = 0 against the alternative Ha:p1 − p2 ≠ 0, the test statistic is found to be 2.2. Which of the following statements can you make about this finding?

The result is significant at both α = 0.05 and α = 0.01.
The result is significant at α = 0.05 but not at α = 0.01.
The result is significant at α = 0.01 but not at α = 0.05.
The result is not significant at either α = 0.05 or α = 0.01.
The result is inconclusive because we don't know the value of p.

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royalroyfan1 royalroyfan1 · Answer 1 · 2017-08-05T04:23:32+02:00

What do you think it is? I will eliminate the last option "inconclusive" because from what I know of statistics, we have enough data to determine where this result is significant at. We must convert this Test Statistic into a P-Value and if the P-Value is greater than 0.01 (alpha), we say it is "significant at 0.01" and if it's also greater at 0.05 (alpha), we say it is "significant at 0.05 and 0.01" I believe. I verified as much as I could with research. We are finding "does not equal" so it is a two-proportions test" meaning that the test statistic probability must be greater than two times the z-table probability value. When z = 1.8, P(z ≠ 1.8) is 0.0359. Multiply this by two as I believe, then this p-value will be 0.0718, which leads me to believe the answer is the First Option that it is significant at 0.01 & 0.05. I ask you to submit this answer and let me know if I was correct in believing so as I would like to know if I was correct myself. Hope I helped.

astha8579 astha8579 · Answer 2 · 2022-01-28T07:51:39+01:00

We need to find the p value to conclude the result about either accepting or rejecting the null hypothesis.

The correct option is
Option E: The result is inconclusive because we don't know the value of p

How to calculate the p value which is necessary in determining the conclusion of hypothesis testing?

In this case of two tailed test for comparison of means of two samples(assuming p1 and p2 are two sample means), we are given the test statistic's value as 2.2

We are not given what were the sample size or how was the population(normal or not normal). These data are necessary to know what type of test statistic was used.

For example, for comparing means of 2 samples, we can use the t test for 2 sample mean but in that too, we need to know the degree of freedom (which is 2 subtracted from sum of both samples' size).

Can we conclude anything about the testing of hypothesis in this case?

Since we cannot conclude the p-value from the data we pertain, we cannot conclude whether the null hypothesis is acceptable or not.

Thus, we have:

Option E: The result is inconclusive because we don't know the value of p

Learn more about null and alternative hypothesis here:

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