4.
Ray is conducting a hypothesis test with the hypotheses
\(\mathrm { H } _ { 0 }\) : There is no association between time of day and number of snacks eaten
\(\mathrm { H } _ { 1 }\) : There is an association between time of day and number of snacks eaten
He calculates expected frequencies correct to two decimal places, which are given in the following table.
| Number of snacks eaten | | |
| \cline { 2 - 5 } | | 0 | 1 | 2 or more |
| \cline { 2 - 4 }
Day | 23.68 | 21.05 | 5.26 | |
| \cline { 2 - 5 } | Night | 21.32 | 18.95 | 4.74 |
| \cline { 2 - 5 } | | | | |
| \cline { 2 - 5 } |
Ray calculates his test statistic using \(\sum \frac { ( O - E ) ^ { 2 } } { E }\)
- State, with a reason, the error Ray has made and describe any changes Ray will need to make to his test.
[0pt]
[3 marks] - Having made the necessary corrections as described in part (a), the correct value of the test statistic is 8.74
Complete Ray's hypothesis test using a \(1 \%\) level of significance.