magnifico99
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- Joined
- Apr 29, 2019
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Hello!
I want to know whether the difference in the two proportions of the two samples (S1 and S2) is greater than 10% at a 5% significance level. Data and my calculations are in the attached picture.
There are two Hypotheses I want to check. Please refer to “Hypothesis 1” and “Hypothesis 2” in the attached picture (for some reasons I cannot upload the MS excel file here, would've been so much more better!)
Hypothesis 1:
Ho: S1-S2 <= 0.1
Ha: S1-S2 > 0.1
As you can see in the calculations, the p-value is greater than 0.05, therefore we do not reject the null, and conclude that the difference in the two proportions is less than 10%.
Hypothesis 2:
Ho: S1-S2 >= 0.1 (Notice that this hypothesis is the opposite of Hypothesis 1.)
Ha: S1-S2 < 0.1
Even here, the p-value is greater than 0.05, therefore we do not reject the null, and conclude that the difference in the two proportions is greater than 10%.
So, my doubt really is this: How can the two Null Hypothesis both be true when they are the opposite of each other? I mean, the difference in proportions cannot be less than 10% AND greater than 10% at the same time. Right?
Of course, I am missing something in my calculations/ knowledge here. Please help me out!
I want to know whether the difference in the two proportions of the two samples (S1 and S2) is greater than 10% at a 5% significance level. Data and my calculations are in the attached picture.
There are two Hypotheses I want to check. Please refer to “Hypothesis 1” and “Hypothesis 2” in the attached picture (for some reasons I cannot upload the MS excel file here, would've been so much more better!)
Hypothesis 1:
Ho: S1-S2 <= 0.1
Ha: S1-S2 > 0.1
As you can see in the calculations, the p-value is greater than 0.05, therefore we do not reject the null, and conclude that the difference in the two proportions is less than 10%.
Hypothesis 2:
Ho: S1-S2 >= 0.1 (Notice that this hypothesis is the opposite of Hypothesis 1.)
Ha: S1-S2 < 0.1
Even here, the p-value is greater than 0.05, therefore we do not reject the null, and conclude that the difference in the two proportions is greater than 10%.
So, my doubt really is this: How can the two Null Hypothesis both be true when they are the opposite of each other? I mean, the difference in proportions cannot be less than 10% AND greater than 10% at the same time. Right?
Of course, I am missing something in my calculations/ knowledge here. Please help me out!
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