A population $\text{(with mean $\mu$)}$ follows normal distribution. Ten samples $(N)$ are drawn at random with a mean value of " $x$ " and standard deviation of " $S$ ". Following table provides the confidence limits, $\mathrm{C}(\mathrm{t})$ of the cumulative probability function for Student's $t$ - distribution two-tailed test with degree of freedom, $\text{D}$
Which one of the following expression is correct for testing the null hypothesis $H_{0}: \mu=0$ at $10 \%$ significance level?
| $\text{D}$ |
$\text{C(t)}$ |
| $0.9$ |
$0.95$ |
$0.975$ |
| $9$ |
$1.38$ |
$1.83$ |
$2.26$ |
| $10$ |
$1.37$ |
$1.81$ |
$2.23$ |
| $11$ |
$1.36$ |
$1.80$ |
$2.20$ |
- $-1.81<\frac{x}{\frac{S}{\sqrt{N-1}}}<1.81$
- $-1.83<\frac{x}{\frac{S}{\sqrt{N-1}}}<1.83$
- $-1.37<\frac{x}{\frac{S}{\sqrt{N-1}}}<1.37$
- $-2.23<\frac{x}{\frac{S}{\sqrt{N-1}}}<2.23$
