Suppose You Conduct A Test And Your P-value Is Equal To 0.13. What Can You Conclude?

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The P-value is a measure of the probability that a hypothesis might have occurred by chance or not. Hence, a P-value of 0.13 means that the hypothesis has occurred by random chance. Therefore, we’ll fail to reject the null hypothesis.

The commonly used α – value is 0.05 ;

The P-value is then compared to the α – value.
If the p-value is lesser than the α – value, then we reject the Null hypothesis otherwise, we fail to reject the null hypothesis.
Therefore, since P-value > α – value, we fail to reject the null hypothesis.

Suppose you conduct a test, and your p-value=0.17. What can you conclude? 

A. Reject Ho at alpha=0.05 but not at alpha =0.10

B. Reject Ho at alpha=0.05 but not at alpha =0.01

C. Reject Ho at alpha =0.10 but not at alpha=0.05

D. Reject Ho at alpha=0.01 but not at alpha=0.05

E. Reject Ho at alpha equal to 0.10, 0.05, and 0.01

F. Do not reject Ho at alpha equal to 0.10, 0.05, and 0.01

Answer

F. Do not reject Ho at alpha equal to 0.10, 0.05, and 0.01.

Given: P-value=0.17  We reject the null hypothesis H_0H  0 ​  , if the P-value is smaller than the significance level \alphaα.  If \alpha=0.01α=0.01, then the P-value is larger than the significance level \alpha=0.01α=0.01 and thus we fail to reject the null hypothesis H_0H  0 ​  .  If \alpha=0.05α=0.05, then the P-value is larger than the significance level \alpha=0.05α=0.05 and thus we fail to reject the null hypothesis H_0H  0 ​  .  If \alpha=0.10α=0.10, then the P-value is larger than the significance level \alpha=0.10α=0.10 and thus we fail to reject the null hypothesis H_0H  0 ​  .  Thus we note that we fail to reject H_0H  0 ​   at all three significance levels and thus the correct answer is:  ANSWER= F. Do no reject Ho at alpha equal to 0.10, 0.05, and 0.01.

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