Lanjutan Contoh Soal 6 Distribusi Normal

$\begin{array}{l}\\ 26.& \text{Untuk menguji hipotesis}\\ & \{\begin{array}{ll}{H}_0& :\mu =16\\ H_1& :\mu >16\end{array}\\ & \text{Jika dalam penelitian terhadap sampel}n=20\\ & \text{diperoleh}\bar{\text{x}}=16,9\text{dengan simpangan baku}\\ & \sqrt{2,3},\text{maka perhitungan nilai statistik ujinya}\\ & \text{adalah}....\\ & \text{a}.z=-2,65\\ & \text{b}.t=-2,65\\ & \text{c}.z=2,65\\ & \text{d}.t=2,65\\ & \text{e}.z=2,95\\ \\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{d}}\\ & \begin{array}{rl}& \underset{―}{\text{Hipotesis (penelitian sampel)}}\\ & {\text{H}}_0:\mu =16\\ & {\text{H}}_0:\mu >16\\ & \text{dengan},n=20,\bar{\text{x}}=16,9,s=\sqrt{2,3}=1,52,\\ & \text{maka}\\ & \text{t}=\left({\displaystyle \frac{\bar{\text{x}}-\mu }{s}}\right)\sqrt{n}={\displaystyle \frac{16,9-16}{1,52}\sqrt{20}}\\ & =\left({\displaystyle \frac{0,9}{1,52}}\right)\times 4,472=2,65\end{array}\end{array}$.

$\begin{array}{l}\\ 27.& \text{Pada soal no.26 di atas, jika taraf nyata}\\ & 0,01,\text{maka kesimpulannya adalah}...\\ & \text{a}.H_0\text{ditolak}\\ & \text{b}.H_0\text{diterima}\\ & \text{c}.H_1\text{diterima}\\ & \text{d}.H_1\text{ditolak}\\ & \text{e}.\text{tidak dapat ditarik kesimpulan}\\ \\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{b}}\\ & \text{Kasus uji satu pihak}\\ & \begin{array}{rl}& \underset{―}{\text{Hipotesis}}\\ & {\text{H}}_0:\mu =16\\ & {\text{H}}_0:\mu >16\\ & \text{dengan}\alpha =0,01=1\mathrm{\%}\Rightarrow t_{0,99}=2,54\\ & \text{Kriteria pengambilan keputusan}:\\ & \text{Tolak}{H}_0\text{jika}t\ge 2,54\end{array}\end{array}$.

$\begin{array}{l}\\ 28.& \text{Seorang petugas}customerservice\text{menyatakan}\\ & \text{bahwa di dealer A dapat mensevis rata-rata }\\ & \text{sebanyak}75\text{unit sepeda motor perhari}.\text{Untuk}\\ & \text{mengecek kebenaran pernyataan di atas diambil}\\ & \text{sampel beberapa hari secara random sebanyak }\\ & \text{20 hari. Dari penelitian ini diperoleh rata-rata}\\ & \text{78 unit dengan simpangan bakunya 5. Hasil}\\ & \text{perhitungan}{\text{z}}_0-\text{nya adalah}....\\ & \text{a}.2,35\\ & \text{b}.2,43\\ & \text{c}.2,55\\ & \text{d}.2,68\\ & \text{e}.2,75\\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{d}}\\ & \begin{array}{rl}& \text{Diketahui data dianggap berdistribusi}\\ & \text{normal baku}N(0,1)\text{dengan}\\ & \text{Rata-rata sampel}=\bar{\text{x}}=78\text{unit sepeda motor}\\ & \text{Rata-rata populasinya yang diuji}={\mu }_0=75\\ & \text{Simpangan bakunya}=\sigma =5\text{unit}\\ & \text{dengan banyak data sampel}=n=20\text{hari}\\ & \text{Penghitungan nilainya}z-\text{nya}\\ & ={\displaystyle \frac{\bar{\text{x}}-{\mu }_0}{{\displaystyle \frac{\sigma }{\sqrt{n}}}}}\\ & ={\displaystyle \frac{78-75}{{\displaystyle \frac{5}{\sqrt{20}}}}={\displaystyle \frac{3}{{\displaystyle \frac{5}{2\sqrt{5}}}}}}\\ & ={\displaystyle \frac{6}{\sqrt{5}}=\frac{6}{2,236}=2,683}\end{array}\end{array}$.

$\begin{array}{l}\\ 29.& \text{Tersiar kabar bahwa harga beras di pasar di}\\ & \text{wilayah B adalah}\text{Rp}8.000,00/\text{Kg dengan}\\ & \text{simpangan baku}\text{Rp}1.500,00.\text{Berdasar kabar}\\ & \text{tersebut dilakukan penelitian dengan mengambil}\\ & \text{sampel secara acak sebanyak}60\text{kios yang dan}\\ & \text{diperoleh rata-rata harga beras}\text{Rp}7.800,00/\text{Kg}\\ & \text{Jika penghitungan menggunakan tingkat}\\ & \text{signifikansi}5\mathrm{\%},\text{maka kesimpulan berikut }\\ & \text{yang tepat adalah}....\\ & \text{a}.\text{harga beras di pasar lebih dari}\text{Rp}7.800,00/\text{Kg}\\ & \text{b}.\text{harga beras di pasar lebih dari}\text{Rp}8.000,00/\text{Kg}\\ & \text{c}.\text{harga beras di pasar kurang dari}\text{Rp}0.000,00/\text{Kg}\\ & \text{d}.\text{harga beras di pasar}\text{Rp}7.800,00/\text{Kg}\\ & \text{e}.\text{harga beras di pasar}\text{Rp}8.000,00/\text{Kg}\\ \\ & \mathbf{\text{Jawab}}:\mathbf{\text{e}}\\ & \begin{array}{rl}& \underset{―}{\text{Hipotesis}}\\ & \text{Rata-rata harga beras dipasar}\text{Rp}8.000,00/\text{Kg}\\ & {\text{H}}_0:\mu =8.000\\ & {\text{H}}_0:\mu \ne 8.000\\ & \underset{―}{\text{Daerah Kritis}}\\ & \text{Taraf nyata yang dipilih adalah}=\alpha =0,05=5\mathrm{\%}\\ & {\displaystyle \frac{\alpha }{2}=2,5\mathrm{\%}=0,025}\\ & {\text{z}}_{0,025}=1,96\\ & \text{maka daerah kritis/penolakannya adalah}\\ & \text{z}<-1,96\text{atau}\text{z}>1,96\end{array}\end{array}$.

$.\begin{array}{rl}& \underset{―}{\text{Nilai Satistik Uji}}\\ & \text{Dihitung dengan rumus}:\text{z}={\displaystyle \frac{\bar{\text{x}}-{\mu }_0}{{\displaystyle \frac{\sigma }{\sqrt{n}}}}}\\ & \text{z}={\displaystyle \frac{7.800-8.000}{{\displaystyle \frac{1.500}{\sqrt{60}}}}=-{\displaystyle \frac{200\sqrt{60}}{1.500}=-1,03}}\\ & \underset{―}{\text{Keputusan Uji}}\\ & \text{Karena nilai}-1,96<\text{z}<1,96,\\ & \text{maka}{\text{H}}_0\text{diterima}\\ & \underset{―}{\text{Kesimpulan}}\\ & \text{Rata-rata harga beras dipasar}\text{Rp}8.000,00/\text{Kg}\end{array}$ .