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 :
Answer & explanation
Correct answer: option 2
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)