"\\mu=10.5, \\sigma=3.5, n=50, \\bar{x} =11.3\\\\\nFormulate\\ the \\ hypothesis\\\\\nH_0:\\mu=10.5\\\\\nH_1:\\mu>10.5\\\\\nThis \\ is \\ a\\ one\\ tailed\\ test\\\\\n\\alpha=0.05\\\\\nSince\\ \\sigma \\ is \\ known\\ we\\ are\\ using\\ the\\ z\\ test\\\\\n1-0.05=0.95,\\ from\\ z-tables\\ we \\ have\\ 1.645\\\\\nThe\\ z\\ critical\\ value(s)\\ is\\ 1.645\\\\\nz=\\frac{\\bar{x}-\\mu}{\\frac{\\sigma}{\\sqrt{n}}}=\\frac{11.3-10.5}{\\frac{3.5}{\\sqrt{50}}}=1.616\\\\\nSince\\ the\\ test\\ statistics\\ is \\,less \\ than\\ the\\ critical\\ value,\\ that\\ is\\ 1.616\\lt1.645\\\\\nWe\\ fail\\ to\\ reject\\ the\\ the\\ null\\ hypothesis\\ and\\ conclude\\ that\\ the\\ new\\ model\\ is\\ not\\ fuel\\ efficient\\\\\n as\\ compared\\ to\\ the\\ old\\ model\\ with\\ average\\ of\\ 10.5km\\ per\\ litre\\ at\\ 5\\%\\ level\\ of significance."
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