Lanjutan Contoh Soal 5 Distribusi Normal

$\begin{array}{ll}\\ 21.&\textrm{Pada suatu kelas seorang guru matematika}\\ &\textrm{menyatakan bahwa nilai ulangan mapel }\\ & \textrm{yang diampunya tidak kurang dari}\: \:68\\ &\textrm{Untuk menentukan uji tersebut, maka guru}\\ &\textrm{yang bersangkutan memilih 10 anak secara}\\ &\textrm{acak untuk ditanyai nilai hasil ulangannya}\\ &\textrm{Hipotesis}\: \: \textrm{H}_{0}\: \: \textrm{dan}\: \: \textrm{H}_{1}\: \: \textrm{yang tepat dari kondisi}\\ &\textrm{kondisi di atas adalah}\:  ....\\ &\textrm{a}.\quad \begin{matrix} \textrm{H}_{0}:\mu =68\\  \textrm{H}_{1}:\mu \neq 68 \end{matrix}\\ &\textrm{b}.\quad \begin{matrix} \textrm{H}_{0}:\mu =68\\  \textrm{H}_{1}:\mu > 68 \end{matrix}\\ &\textrm{c}.\quad \color{red}\begin{matrix} \textrm{H}_{0}:\mu \geq 68\\  \textrm{H}_{1}:\mu < 68 \end{matrix}\\ &\textrm{d}.\quad \begin{matrix} \textrm{H}_{0}:\mu \leq 68\\  \textrm{H}_{1}:\mu >q 68 \end{matrix}\\ &\textrm{e}.\quad \begin{matrix} \textrm{H}_{0}:\mu >68\\  \textrm{H}_{1}:\mu \neq 68 \end{matrix}\\\\ &\textbf{Jawab}:\quad \textbf{c}\\ &\textrm{Cukup jelas}\\ &\textrm{Dan ini contoh uji satu pihak, yaitu kiri}  \end{array}$.

$\begin{array}{ll}\\ 22.&\textrm{Untuk menguji hipotesis}\\ &\begin{cases} H_{0} &: \mu =800 \\  H_{1} &: \mu \neq 800  \end{cases}\\ &\textrm{Jika dalam penelitian didapatkan}\: \overline{\textrm{x}}=795\\ &\textrm{dan}\: \: n=100\: \: \textrm{serta simpangan baku}\\ &\textrm{populasi}\: \: 55,\: \textrm{maka perhitungan nilai}\\ &\textrm{statistik ujinya adalah}\: ....\\  &\textrm{a}.\quad z=-1,10\\ &\textrm{b}.\quad \color{red}z=-0,91\\ &\textrm{c}.\quad t=-0,91\\ &\textrm{d}.\quad t=0,91\\ &\textrm{e}.\quad z=0,91\\\\\\ &\textbf{Jawab}:\quad \textbf{b}\\ &\begin{aligned}&\underline{\textrm{Hipotesis}}\\ &\textrm{H}_{0}:\mu =800\\ &\textrm{H}_{0}:\mu \neq 800\\ &\textrm{dengan},\: n=100,\: \overline{\textrm{x}}=795,\: \sigma =55,\: \textrm{maka}\\ &\: \textrm{z}\: \: =\left (\displaystyle \frac{\overline{\textrm{x}}-\mu  }{\sigma }  \right )\sqrt{n}=\displaystyle \frac{795-800}{55}\sqrt{100}\\&\quad =\left (\displaystyle \frac{-5}{55}  \right )\times 10=\color{red}-0,91 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 23.&\textrm{Pada soal no.22 di atas, jika taraf nyata}\\ &5\%,\: \textrm{maka kesimpulannya adalah}\: ...\\  &\textrm{a}.\quad H_{0}\: \: \textrm{ditolak}\\ &\textrm{b}.\quad \color{red}H_{0}\: \: \textrm{diterima}\\ &\textrm{c}.\quad H_{1}\: \: \textrm{diterima}\\ &\textrm{d}.\quad H_{1}\: \: \textrm{ditolak}\\ &\textrm{e}.\quad \textrm{tidak dapat ditarik kesimpulan}\\\\\\ &\textbf{Jawab}:\quad \textbf{b}\\ &\textrm{Kasus uji dua pihak}\\ &\begin{aligned}&\underline{\textrm{Hipotesis}}\\ &\textrm{H}_{0}:\mu =800\\ &\textrm{H}_{0}:\mu \neq 800\\ &\textrm{dengan}\: \alpha =5\%=0,05\Rightarrow z_{\frac{1}{2}(1-0,05)}\\ &\quad =z_{0,475}=1,96 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 24.&\textrm{Untuk menguji hipotesis}\\ &\begin{cases} H_{0} &: \mu =20 \\  H_{1} &: \mu <20  \end{cases}\\ &\textrm{Jika dalam penelitian terhadap sampel}\: n=21\\ &\textrm{diperoleh}\: \: \overline{\textrm{x}}=19,8\: \: \textrm{dengan simpangan baku}\\ &0,4,\: \textrm{maka perhitungan nilai statistik ujinya}\\ &\textrm{adalah}\: ....\\  &\textrm{a}.\quad z=-2,29\\ &\textrm{b}.\quad \color{red}t=-2,29\\ &\textrm{c}.\quad z=2,29\\ &\textrm{d}.\quad t=2,29\\ &\textrm{e}.\quad z=2,99\\\\\\ &\textbf{Jawab}:\quad \textbf{b}\\ &\begin{aligned}&\underline{\textrm{Hipotesis (penelitian sampel)}}\\ &\textrm{H}_{0}:\mu =20\\ &\textrm{H}_{0}:\mu <20\\ &\textrm{dengan},\: n=21,\: \overline{\textrm{x}}=19,8,\: s =0,4,\: \textrm{maka}\\ &\: \textrm{t}\: \: =\left (\displaystyle \frac{\overline{\textrm{x}}-\mu  }{s}  \right )\sqrt{n}=\displaystyle \frac{19,8-20}{0,4}\sqrt{21}\\&\quad =\left (\displaystyle \frac{-0,2}{0,4}  \right )\times 4,5828=\color{red}-2,29 \end{aligned} \end{array}$.

$\begin{array}{ll}\\ 25.&\textrm{Pada soal no.24 di atas, jika taraf nyata}\\ &0,01,\: \textrm{maka kesimpulannya adalah}\: ...\\  &\textrm{a}.\quad H_{0}\: \: \textrm{ditolak}\\ &\textrm{b}.\quad \color{red}H_{0}\: \: \textrm{diterima}\\ &\textrm{c}.\quad H_{1}\: \: \textrm{diterima}\\ &\textrm{d}.\quad H_{1}\: \: \textrm{ditolak}\\ &\textrm{e}.\quad \textrm{tidak dapat ditarik kesimpulan}\\\\\\ &\textbf{Jawab}:\quad \textbf{b}\\ &\textrm{Kasus uji satu pihak}\\ &\begin{aligned}&\underline{\textrm{Hipotesis}}\\ &\textrm{H}_{0}:\mu =20\\ &\textrm{H}_{0}:\mu < 20\\ &\textrm{dengan}\: \alpha =0,01=1\%\Rightarrow t_{0,99}=2,53\\ &\textrm{Kriteria pengambilan keputusan}:\\ &\textrm{Tolak}\: \: H_{0}\: \: \textrm{jika}\: \: t\leq \color{red}-2,53 \end{aligned} \end{array}$.