Question

Suppose you conduct a hypothesis test based on a sample where the sample size is n = 50, and arrive at a p-value of 0.08. You then refer back to your notes and discover that you made a careless mistake, the sample size should have been n = 500. Will your p-value increase, decrease, or stay the same?

• stay the same
• decrease
• increase

Answer 1

Solution :-

In hypothesis testing,

As the sample size Increases, P- value Decreases.

In Hypothesis, As the sample size increases, Z score or t score increases and corresponding P - value decreases.

In above case,when n = 50 , P-value = 0.08 but when n= 500 ( i.e n increases from 50 to 500 ) P - value will become smaller than 0.08.

In statistics, the p-value is the probability of obtaining the observed results of a test, assuming that the null hypothesis is correct. P-values are calculated using p-value tables or spreadsheets/statistical software.The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis.

P values are affected by the effect size and the sample size; if you keep the effect size constant, a larger sample will yield a smaller p value.