[填空题]
Every year a sports academy en2rfj3vgx/c v /rols new memj-pbfti,,tb0xh ;h. mbers from a large group of applicants. This year the academy enrols 100 new members from whom the t;,,mphbh tf-xi .jb 0academy records some data and conducts several tests.
A staff member wonders if there exists some relationship between the age and the EQ (emotional intelligence) of new members. The data recorded is shown in the following table.
1. $A \chi^{2}$ test is performed at the $5 \%$ significant level to determine whether the EQ test result is independent of age.
1. State the null and alternative hypotheses for this test.
2. Determine the number of degrees of freedom for this test.
3 . Find the p -value for this test.≈
4. Write down the conclusion to the test.
From the total of 100 new members enrolled, 34 selected tennis, and 66 selected volleyball as their sport of choice. A sample of 30 new members is selected to participate in a sports competition. The sample will contain the same proportion of tennis and volleyball players as the population of 100 new members.
2. Show that 10 tennis members were selected for the competition.≈
3. The selected members that play tennis each stayed in a different hotel during the competition. The following table shows the star rating of each hotel and the average guest satisfaction scored on a 100 point scale.
1. Find the Pearson's product moment correlation coefficient, r .≈
2. Interpret the value found in part (i).
3. Find the Spearman's rank correlation coefficient, $r_{s}$ .≈
4. Interpret the value found in part (iii).
5. In the context of this question, comment if both correlation coefficients should be considered when determining the relationships between guest satisfaction and the star rating of hotels or if one should be used instead of the other.
The selected tennis group is tested on motor skills twice, at the beginning and after the tournament to measure its reliability. Results are shown in the following table.
4. 1. State the name of this type of test for reliability.
2. Find the Pearson's product moment correlation coefficient, r .≈
3. Interpret the value found in part (ii).
4. Hence, comment on the reliability of the motor abilities test.
5. Determine at the $5 \% $ level whether the test indicates that the selected tennis group improved their motor skills during the tournament.
