Question

Suppose you are conducting a hypothesis test where the sample size is 49. Now, you want to conduct another hypothesis test on a different sample, where the sample size is 121. The p-value calculated in the first case comes out to be 0.0512. What will happen to the p-value in the second case if you observe the same values for the sample mean and the sample standard deviation for both the cases?

Answer 1

Answer:

It will decrease.

Step-by-step explanation:

• With an increase in the sample size, the denominator of the Z-score decreases, and thus, the absolute value of Z-score increases, which means that the sample mean would move away from the central tendency towards the tails.

• This means that the p-value would actually decrease. Conceptually, increasing the sample size will make the distribution of the sample means narrower, and chances of the sample mean falling in the critical region increase. So, the p-value will decrease.