Question

1a) Explain why we fail to reject the null hypothesis when the p-value is greater than the level of significance.

b) If the null hypothesis is rejected at a level of significance of 5%, does it automatically get rejected at a level of significance of 1%? Explain your reasoning with an example using a p-value(s) that you make up for different scenarios.

c) If the null hypothesis is rejected at a level of significance of 1%, does it automatically get rejected at a level of significance of 5%? Explain your reasoning with an example using a p-value(s) that you make up for different scenarios.

Answer 1

a) Explain why we fail to reject the null hypothesis when the p-value is greater than the level of significance.

the p-value indicates the probability of rejecting the null hypothesis when it is true for a particular set of data.

If this probability is less than that of the threshold type I error probability ( alpha ) we reject the null hypothesis, but of the value exceeds alpha we fail to reject the null hypothesis, in order to meet the threshold.

b) If the null hypothesis is rejected at a level of significance of 5%, does it automatically get rejected at a level of significance of 1%? Explain your reasoning with an example using a p-value(s) that you make up for different scenarios.

No, this does not necessarily hold that the null hypothesis will be rejected for 1% los if it is already rejected for 5% los.

Take example of p-value equals to 0.0345. Here, if we compare it with 5% or 0.05 value of alpha the null hypothesis is rejected since p = 0.0345 is less than alpha but if we compare the same with 1% or 0.01 the p-value > alpha and we failed to reject null hypothesis

c) If the null hypothesis is rejected at a level of significance of 1%, does it automatically get rejected at a level of significance of 5%? Explain your reasoning with an example using a p-value(s) that you make up for different scenarios.

Yes, this is true that if the null hypothesis is rejected at a level of significance of 1%, does it automatically get rejected at a level of significance of 5%

Take example of p-value equals to 0.00345. Here, if we compare it with 1% or 0.01 value of alpha the null hypothesis is rejected since p = 0.00345 is less than alpha also if we compare the same with 5% or 0.05 the p-value > alpha and we reject the null hypothesis