Question

# A survey on men and women’s shopping behavior collected data from a sample of 50 men...

1. 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)

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 Flower = 0.567 < F = 0.774 < FU​pper = 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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