The decision rule in a null hypothesis significance test hinges on comparing the p-value to the pre-determined significance level, denoted by $\alpha$. The null hypothesis (H₀) is rejected if the p-value is less than or equal to the significance level ($\alpha$).
Hypothesis Rejection Rule
The condition for rejecting the null hypothesis is:
$ p \le \alpha $
Significance Level ($\alpha$)
In this specific test, the significance level was set as:
$ \alpha = 0.01 $
Evaluating p-values for Rejection
We examine each provided p-value to see if it meets the rejection criterion ($p \le 0.01$):
- p = 0.004: Since $0.004 \le 0.01$, the null hypothesis is rejected. This corresponds to option A.
- p = 0.02: Since $0.02 > 0.01$, the null hypothesis is not rejected.
- p = 0.10: Since $0.10 > 0.01$, the null hypothesis is not rejected.
- p = 0.009: Since $0.009 \le 0.01$, the null hypothesis is rejected. This corresponds to option D.
Therefore, the null hypothesis would be rejected for p-values of $0.004$ and $0.009$.
Important Questions from Probability
Two dice are thrown simultaneously. What is the probability of getting the same number on both the dice?
The probability of being 53 Sundays in year 2020 is-
Three dice are thrown randomly. The probability of coming 3 in at least one die is
The probability of having 53 Tuesdays in an ordinary year is:
When two dice are tossed simultaneously, the probability that the sum of the numbers appearing on both the dice is 8 will be
