Question

It has been suggusted that the highest priority of retirees is travel. Thus, a study was conducted to investigate the differences in the length of stay of a trip for pre- and post-retirees. A sample of 700 travelers were asked how long they stayed on a typical trip. The observed results of the study are found below. Number of Nights Pre-retirement Post-retirement Total 4−7 238 172 410 8−13 84 62 146 14−21 33 58 91 22 or more 17 36 53 Total 372 328 700 With this information, construct a table of estimated expected values. Number of Nights Pre-retirement Post-retirement 4−7 8−13 14−21 22 or more Now, with that information, determine whether the length of stay is independent of retirement using α=0.05. (a) χ2= (b) Find the degrees of freedom: (c) Find the critical value: (d) The final conclusion is A. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent. B. There is not sufficient evidence to reject the null hypothesis that the length of stay is independent of retirement.

Answer #1

a)

Applying chi square test:

Expected |
E_{i}=row total*column
total/grand total |
Pre | Post | Total |

4-7 | 217.886 | 192.114 | 410 | |

8-13 | 77.589 | 68.411 | 146 | |

14-21 | 48.360 | 42.640 | 91 | |

22 or more | 28.166 | 24.834 | 53 | |

total | 372 | 328 | 700 | |

chi square χ^{2} |
=(O_{i}-E_{i})^{2}/E_{i} |
Pre | Post | Total |

4-7 | 1.857 | 2.106 | 3.963 | |

8-13 | 0.530 | 0.601 | 1.131 | |

14-21 | 4.879 | 5.533 | 10.412 | |

22 or more | 4.426 | 5.020 | 9.447 | |

total | 11.692 | 13.260 | 24.952 |

χ2= 24.952

b)

degree of freedom(df) =(rows-1)*(columns-1)= | 3 |

c)

for 3 df and 0.05 level of signifcance critical value χ2= | 7.815 |

d)

A. We can reject the null hypothesis that the length of stay is independent of retirement and accept the alternative hypothesis that the two are dependent.

It has been suggusted that the highest priority of retirees is
travel. Thus, a study was conducted to investigate the differences
in the length of stay of a trip for pre- and post-retirees. A
sample of 694 travelers were asked how long they stayed on a
typical trip. The observed results of the study are found
below.
Number of Nights
Pre-retirement
Post-retirement
Total
4−7
237
163
400
8−13
79
72
151
14−21
40
56
96
22 or more
10
37...

It has been suggusted that the highest priority of retirees is
travel. Thus, a study was conducted to investigate the differences
in the length of stay of a trip for pre- and post-retirees. A
sample of 672 travelers were asked how long they stayed on a
typical trip. The observed results of the study are found below.
Number of Nights Pre-retirement Post-retirement Total 4−7 231 161
392 8−13 76 67 143 14−21 36 53 89 22 or more 15 33...

It has been suggusted that the highest priority of retirees is
travel. Thus, a study was conducted to investigate the differences
in the length of stay of a trip for pre- and post-retirees. A
sample of 675675 travelers were asked how long they stayed on a
typical trip. The observed results of the study are found
below.
Number of Nights
Pre-retirement
Post-retirement
Total
4−7
230
161
391
8−13
84
60
144
14−21
34
57
91
22 or more
13
36...

(1 point) It has been suggusted that the highest priority of
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Post-retirement
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245245
171171
416416
8−138−13
8282
6868
150150
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3535
6060
9595
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