Consider the following hypothesis test :

A sample of 50 provided a sample mean of 14.15 and standard deviation is 3.

Then, which of the following is true ?

(A) $\mu_0= 15, n=50, \overline{x}=14.15, σ = 3$

(B) $n= 15, \mu_0= 50, σ =14.15, \overline{x}=3$

(C) Test statistic is given by $z=\frac{\overline{x}-\mu_0}{\frac{σ }{\sqrt{n}}}$

(D) $z=\frac{14.15-15}{\frac{3}{\sqrt{50}}}$

(E) $z=\frac{50-15}{\frac{3}{\sqrt{14.15}}}$

Choose the correct answer from the options given below :

(A), (C), (D) only

The correct answer is Option (2) → (A), (C), (D) only

Null Hypothesis, $H_0 : \mu =15$

Alternative Hypothesis, $H_a : \mu ≠ 15$

Sample size, $n=50$

Sample Mean, $\bar x=14.15$

Sample Standard Deviation, $σ=3$  → (A)

t-test statistic formula is,

$z=\frac{\overline{x}-\mu_0}{\frac{σ }{\sqrt{n}}}$ → (C) 

$=\frac{14.15-15}{\frac{3}{\sqrt{50}}}$  → (D)