[填空题]
Applicants to a special divisge2r (kqehtbr8+ spyuch r-2:y a4*a, ion in the Australian Military w(gfw7o6 . wtcForces need to undertake a fitness test with five components: Sprint, Enduragt6w .w f(7wocnce Run, Push-Ups, Pull-Ups and Squats. Their fitness level on each component is classified as either "At Standard" or "Below Standard". To pass the test, applicants must perform at an At Standard fitness level in each of the five components. In increase intake this year, it was decided that applicants were allowed to omit any one of the five components to increase their chances to pass the test.
The table below shows the number of At Standard and Below Standard performances in each component.
1. A military officer assesses the results and chooses a performance at random. Find the probability that this randomly chosen performance is
1. a performance in Sprint;
2. a Below Standard performance in Sprint;
3. a Below Standard performance, given that it is a performance in Sprint. ≈
2. The military officer groups the performances by component and chooses three performances in Squats. Find the probability that all three are At Standard fitness level.
A $\chi^{2}$ test is carried out at the 5 $\%$ significance level for the data in the table. ≈
3. State the null hypothesis for this test.
4. Show that the expected frequency of Below Standard performances in Sprint is 8 .
5. Write down the number of degrees of freedom for this test.
6. Use your graphic display calculator to find the $\chi^{2}$ statistic for this data.
The critical value for this test is 9.488 .$x^2$ ≈
7. State the conclusion of this $\chi^{2}$ test. Give a reason for your answer.
