Question

Smartphone Users. A Ring Central survey of 380 smartphone users showed that 152 of them said that theirsmartphone is the only thing they could not live without. Use a 0.01 significance level to test the claim thatfewer than half of smartphone users identify the smartphone as the only thing they could not live without

Answer #1

null Hypothesis: Ho: p= | 0.500 | |||

alternate Hypothesis: Ha: p < | 0.500 | |||

for 0.01 level and left tailed test , critical z= | -2.33 |
(from excel:normsinv(0.01) |
||

Decision rule : reject Ho if test statistic z
< 2.33 |

sample success x = | 152 | |

sample size n = | 380 | |

std error σp =√(p*(1-p)/n) = | 0.0256 | |

sample prop p̂ = x/n=152/380= | 0.4000 | |

z =(p̂-p)/σp=(0.4-0.5)/0.026= |
-3.90 |

since test statistic falls in rejection region we reject null hypothesis |

we have sufficient evidence to conclude that fewer than half of smartphone users identify the smartphone as the only thing they could not live without |

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