91影视

A random sample of X₁,鈥︹��.., X_n is to be taken from the normal distribution.

Need to test,

H₀ : 碌 鈮� 3

H₁: 碌 >3

With the sample size of n = 17, the sample variance (with denominator n-1) is

\begin{aligned}s^{2}=\frac{n}{n-1}\times\frac{1}{n}\sum_{i-1}^{n}(X_{i}-\overline{X})^{2}\end{aligned}

\begin{aligned}=\frac{17}{16}\times0.09\end{aligned}

The T statistic U is now as follows:

\begin{aligned}U=\frac{\sqrt{n}\overline{X}-3}{s}\end{aligned}

\begin{aligned}=\frac{\sqrt{17}\times0.2}{\sqrt{\frac{17}{16}}\times 0.9}\end{aligned}

\begin{aligned}=\frac{0.2\times4}{0.3}\end{aligned}

\begin{aligned}=\frac{8}{3}\end{aligned}

Thus, U=8/3

The U statistic now follows a T distribution with n-1=16 degrees of freedom at 碌 = 3

As a result, the p values are provided by

P(U>8/3|碌 = 3) =0.008

A p-value is obtained by using the t table for 16 degrees of freedom.