Question

Markets have become interested in the potential of social networking sites. But they need to understand the demographics of social networking users. A research company conducted a survey in late 2012 that asked about social networking over several years and for different age groups. A table of responses is shown to the right

May 2010 Aug 2011 Aug 2012 total

18-29 274 280 309 863

30-49 323 352 379 1054

50-64 258 282 321 861

Total 855 914 1009 2778

-----The expected values are:

18-29: 265.61 283.94 313.45

30-49 324.40 346.78 382.82

50-64 264.99 283.28 312. 72

a) Compute the x2 statistic

b) How many degree of freedom foes x2 statistic have?

c) Find the critical value where alpha = 0.05

Answer #1

applying chi square test on above data:

Observed | OBS | may -2000 | aug-2011 | aug-2012 | Total |

18-29 | 274 | 280 | 309 | 863 | |

30-49 | 323 | 352 | 379 | 1054 | |

50-64 | 258 | 282 | 321 | 861 | |

Total | 855 | 914 | 1009 | 2778 | |

Expected | E_{i}=?row*?column/?total |
may -2000 | aug-2011 | aug-2012 | Total |

18-29 | 265.610 | 283.940 | 313.450 | 863 | |

30-49 | 324.400 | 346.780 | 382.820 | 1054 | |

50-64 | 264.990 | 283.280 | 312.720 | 860.99 | |

Total | 855 | 914 | 1008.99 | 2777.99 | |

chi square | =(O_{i}-E_{i})^{2}/E_{i} |
may -2000 | aug-2011 | aug-2012 | Total |

18-29 | 0.27 | 0.05 | 0.06 | 0.38 | |

30-49 | 0.01 | 0.079 | 0.038 | 0.12 | |

50-64 | 0.18 | 0.006 | 0.219 | 0.41 | |

Total | 0.46 | 0.14 | 0.32 | 0.915 |

a) x2 statistic =0.915

b)degree of freedom =(rows-1)*(column-1)=(3-1)*(3-1)=4

c) for 4 df and 0.05 level critical value =9.488

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