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So I want to know when do we accept the null hypothesis and when we don't in t test.

Case 1: t cal>t tab and p value >0.05,we accept null hypothesis

Case 2: t cal>t tab and p value <0.05 we don't accept null hypothesis.

Case 3: t cal < t tab and p value <0.05,we accept null hypothesis

Case 4: t cal < t tab and p value >0.05,we accept null hypothesis

It this correct?

prishila
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1 Answers1

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The rule is

low $p$-value $\Leftrightarrow$ reject the null hypothesis.

So if $p\le 0.05$ (or whatever significance level you set), then you can reject the null hypothesis. Otherwise, you cannot reject it. Currently, you have written $p<0.05$ in all cases, which is not correct.

Minus One-Twelfth
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  • Sorry, I corrected it. But it p value is low and t cal < t tab, then do we still reject null hypothesis? I think we don't because the t we get is between the critic values, where null hypothesis is accepted. I am talking about t test. – prishila May 25 '19 at 10:07
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    If your p-value is low, it means your $t_{cal}$ must be such that you should reject the null hypothesis. If you are testing a null hypothesis $H_0:μ=μ0$ vs. $H_1:μ<μ_0$ for example, then $t{cal}$ will be less than $t_{tab}$ if and only if the $p$-value is low. If you are testing $H_0:μ=μ0$ vs. $H_1:μ > μ_0$ , then the $p$-value won't be low if $t{cal} < t_{tab}$, since "extreme" values of the $t$ statistic here are when $t_{cal} >t_{tab}$ (so for this hypothesis test, $t_{cal} > t_{tab}$ is when the $p$-value will be low). – Minus One-Twelfth May 25 '19 at 12:40