Question

Given below are two statements.
Assertion (A):
A random sample of size \(25\) is taken, resulting in a sample mean of \(17.45\) and a sample standard deviation of \(3.6\). Assuming \(H_0:
\mu=18,\ H_1:
\mu\neq18\), the standard error calculated is \(0.72\).
Reason (R):
The standard error for hypothesis testing is calculated using \(\frac{s}{\sqrt{n}}\).

• A. Both (A) and (R) are correct and (R) is the correct explanation of (A)
• B. Both (A) and (R) are correct but (R) is not the correct explanation of (A)
• C. (A) is correct but (R) is not correct
• D. (A) is not correct but (R) is correct

Hint:

Standard error decreases as sample size increases because \(SE=\frac{s}{\sqrt{n}}\).

Answer 1

The Correct Option is A

Concept:
Standard error of mean is: \[ SE=\frac{s}{\sqrt{n}} \]

Step 1: Identify values. \[ s=3.6,\quad n=25 \]

Step 2: Apply the formula. \[ SE=\frac{3.6}{\sqrt{25}} \] \[ SE=\frac{3.6}{5} \] \[ SE=0.72 \] Thus, Assertion is correct. Reason gives the correct formula and explains Assertion. \[ \therefore \text{Correct Answer is (A)} \]