Question

- A survey on men and women’s shopping behavior collected data from a sample of 50 men and 50 women. The following data on online shopping spending every month.

Men | Women |

148 | 272 |

211 | 176 |

256 | 251 |

309 | 235 |

190 | 145 |

205 | 179 |

203 | 30 |

208 | 135 |

231 | 200 |

125 | 270 |

149 | 174 |

205 | 123 |

195 | 199 |

178 | 195 |

196 | 192 |

198 | 102 |

110 | 110 |

199 | 184 |

181 | 228 |

168 | 316 |

218 | 170 |

222 | 234 |

206 | 163 |

168 | 245 |

239 | 174 |

130 | 126 |

246 | 227 |

149 | 86 |

262 | 96 |

142 | 185 |

174 | 288 |

181 | 154 |

198 | 217 |

147 | 184 |

143 | 154 |

185 | 217 |

200 | 222 |

166 | 175 |

171 | 265 |

133 | 196 |

295 | 172 |

242 | 113 |

299 | 240 |

209 | 235 |

189 | 269 |

173 | 243 |

109 | 131 |

291 | 134 |

208 | 56 |

227 | 164 |

Treat the men as population 1 and the
women as population 2. Formulate the null and alternative
hypotheses and test whether there is evidence of a difference in
the variances of monthly online shopping spending between men and
women. Please follow the hypothesis testing steps in arriving at a
decision. You must show all the calculations in the spreadsheet.
*(15 points)*

Answer #1

The provided sample variances are and and the sample sizes are given by and .

The following null and alternative hypotheses need to be tested:

This corresponds to a two-tailed test, for which a F-test for two population variances needs to be used.

The significance level is α=.05, and the the rejection region for this two-tailed test is R={F:F<0.567 or F>1.762}.

*Test
Statistics*

The F-statistic is computed as follows:

As F_{lower} = 0.567 < F = 0.774 <
F_{Upper} = 1.762, it is then concluded that *the null
hypothesis is not rejected.*

It is concluded that the null hypothesis Ho is *not
rejected.* Therefore, there is not enough evidence to claim
that there is difference in the variances of monthly online
shopping spending between men and women.

**Excel formulae: Data is in column DC and DD; DC3:DC52;
DD3:DD52. F-statistics is ratio of sample variance.**

Sample Variance(Men) |
Sample Variance(Women) |
F-Value |
Lower Critical Value |
Upper Critical Value |

=STDEV.S(DC3:DC52) |
=STDEV.S(DD3:DD52) |
=DE3/DF3 |
=F.INV(0.025,49,49) |
=F.INV(0.975,49,49) |

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