5 Gloria is a market trader who sells jeans. She trades on Mondays, Wednesdays and Fridays. Wishing to investigate whether the volume of trade depends on the day of the week, Gloria analysed a random sample of 150 days' sales and classified them by day and volume (low, medium and high). The results are given in the table below.
| | Day |
| | Monday | Wednesday | Friday |
| \multirow{3}{*}{Volume} | Low | 15 | 13 | 2 |
| Medium | 23 | 26 | 23 |
| High | 12 | 9 | 27 |
Gloria asked a statistician to perform a suitable test of independence and, as part of this test, expected frequencies were calculated. These are shown in the table below.
| | Day |
| | Monday | Wednesday | Friday |
| Low | 10.00 | 9.60 | 10.40 |
| Volume | Medium | 24.00 | 23.04 | 24.96 |
| High | 16.00 | 15.36 | 16.64 |
- Show how the value 23.04 for medium volume on Wednesday has been obtained.
- State, giving a reason, if it is necessary to combine any rows or columns in order to carry out the test.
The value of the test statistic is found to be 21.15, correct to 2 decimal places.
- Stating suitable hypotheses for the test, give its conclusion using a \(1 \%\) significance level.
Gloria wishes to hold a sale and asks the statistician to advise her on which day to hold it in order to sell as much as possible.
- State the day that the statistician should advise and give a reason for the choice.