Question

The Pew Research Centers Internet and American Life project surgery of 2,252 American Adults, ages 18 years and older, conducted January 20, 2012 - February 19, 2011, revealed that 46% of American adults own a smartphone of some kind

A) Perform the two (2) checks necessary for determining the confidence interval for the proportion go American adults who own a smartphone. For each check, clearly state the conclusion using 1 sentence. You must use appropriate notation.

B) Determine and state the 98% confidence interval for the proportion of American adults who own a smartphone.

C) Using one sentence, interpret the 98% confidence interval in the context of this scenario.

Answer #1

a)

conditions for normality | |

n | p |

2252 | 0.46 |

np | 1035.92 |

nq | 1216.08 |

np(1-p) | 559.3968 |

both np and nq > 5

hence normal approximation is appropriate

b)

X | 1035.92 |

n | 2252 |

p | 0.460 |

q | 0.540 |

alpha | 0.02 |

z | 2.326348 |

E | 0.0244 |

lower | 0.436 |

upper | 0.484 |

98% confidence interval is (0.436,0.484)

c)

we are 98% confident that true proportion of American adults who own a smartphone lies in this confidence interval

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