100 randomly selected items were tested. It was found that 40 of the items tested positive.

Test the hypothesis that exactly 50% of the items tested positive at α = 0.05

H

H

p^ = | x |

n |

p^ = | 40 |

100 |

p^ = 0.4

z = | p^ - p |

√p(1 - p)/n |

z = | 0.4 - 0.5 |

√0.5(1 - 0.5)/100 |

z = | -0.1 |

√0.5(0.5)/100 |

z = | -0.1 |

√0.0025 |

z = | -0.1 |

0.05 |

z = -2

Z = 1.6449

Our rejection region is Z > 1.6449

Since our test statistic of -2 is less than our Z-value of 1.6449, it is not in the rejection region, so we accept H