## QUESTION 1 A swimming coach wants to know whether swimmers showed improvement in 100 meter...

**QUESTION 1**

A swimming coach wants to know whether swimmers showed improvement in 100 meters freestyle event after attending a central training camp. As such, 12 swimmers were selected at random and their times were recorded twice: best time before attending the training camp and best time after attending the training camp. The objective of the study is to see whether the times recorded are faster (lower) after attending the training camp as compared to before attending. The times recorded (in seconds) are shown in Table 1.

Table 1

Swimmer | Before | After |

1 | 81.32 | 76.48 |

2 | 69.35 | 66.18 |

3 | 70.65 | 65.15 |

4 | 77.53 | 74.82 |

5 | 86.68 | 77.69 |

6 | 75.37 | 69.42 |

7 | 68.43 | 67.34 |

8 | 64.10 | 55.17 |

9 | 83.28 | 87.40 |

10 | 88.85 | 84.73 |

11 | 61.47 | 59.34 |

12 | 99.96 | 82.04 |

- Calculate the mean time difference after and before attending the training camp.
- Calculate the standard deviation time difference after and before attending the training camp.
- What assumptions should be made to conduct the hypothesis test?
- At a = 0.05, can you support the claim that the mean time after attending the training camp is lower as compared to before attending the training camp? Assume the population variances are equal.

**[20 marks]**

**QUESTION 2**

A second semester class is studying the environment. One of the assignments is to grow bean plants in different soils. Ahmad chose to grow his bean plants in soil found outside his classroom mixed with dryer lint. Wong chose to grow her bean plants in potting soil bought at the local nursery. Lethmi chose to grow his bean plants in soil from his mother's garden. They were grown inside the classroom next to a large window. At the end of the growing period, each plant was measured, producing the data (in cm).

Table 2

Ahmad's Plants | Wong's Plants | Lethmi's Plants |

24 21 23 30 23 | 25 31 23 20 - | 23 27 22 30 20 |

- Construct a complete Analysis of Variance table.
- At a = 0.05, test whether the three soils in which the bean plants were grown produce the same mean height.

**QUESTION 3**

Literacy rate is a reflection of the educational facilities and quality of education available in a country, and mass communication plays a large part in the educational process. In an effort to relate the literacy rate of a country to various mass communication factors, a researcher has proposed to relate literacy rate (* y*) to the following variables: number of daily newspaper copies (per 1000 population)(

*), number of radios (per 1000 population)(*

*x1**), and number of TV sets (per 1000 population)(*

*x2**). Table 3 shows the data for a sample of 10 countries.*

*x3*Table 3

Country | Newspapers | Radios | TV sets | Literacy Rate |

Malaysia | 280 | 266 | 228 | 0.98 |

Singapore | 142 | 230 | 201 | 0.93 |

Vietnam | 10 | 114 | 2 | 0.25 |

Brunei | 391 | 313 | 227 | 0.99 |

Thailand | 86 | 329 | 82 | 0.79 |

Cambodia | 17 | 42 | 11 | 0.72 |

Myanmar | 21 | 49 | 16 | 0.32 |

Indonesia | 314 | 1695 | 472 | 0.99 |

Philippines | 333 | 430 | 185 | 0.99 |

Laos | 91 | 182 | 89 | 0.82 |

- Use Microsoft Excel to produce Analysis of Variance table for the multiple linear regression and state the model.
- At a = 0. 05 test whether the model generated in (a) is fit or not.
- Calculate the 95% confidence interval for the coefficient value for newspapers.
- Interpret the value of
*R*gathered in (a).^{2} - Based on your answer in (b), draw a conclusion on the linear relationship between literacy rate and the three factors.

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