### Answer All Questions

#### Question 1:

Many people sleep late on the weekends to make up for “short nights” during the work week. The Better Sleep council reports that 61% of us get more than 7 hours of sleep per night on the weekend. A random sample of 350 adults found that 235 had more than 7 hours of sleep each night last weekend. At the 0.05 level of significance, does this evidence show that more than 61% sleep 7 hours or more per night on the weekend?

#### Question 2:

For years, many large companies in Melbourne have used a reputable employment agency for testing perspective employees. The employment selection test used has historically resulted in scores of normally distributed about a mean of 82 and a standard deviation of 8. A competitor has developed a new psychoanalytic test that it claims to be quicker and easier to administer and therefore less expensive. The competitor claims that its test results are the same as those obtained by the reputable agency test. Many of the large companies, facing the financial crunch, are considering a change to cut costs. However, they are unwilling to change if the competitor firm’s test results have a different mean value. An independent testing firm tested 36 prospective employees with the Brown test. A sample mean of 70 resulted. Determine the p value associated with this hypothesis test. (Assume population standard deviation to be 8).

#### Question 3:

On a popular self-image test that results in normally distributed scores, the mean score for public-assistance recipients is expected to be 65. A random sample of 28 public assistance recipients in NTG is given the test. They achieve a mean score of 62.1, and their scores have a standard deviation of 5.83. Do the NTG public assistance recipients test differently on average, than what is expected, at the 0.02 level of significance?

#### Question 4:

College students have regularly insisted on freedom of choice when they register for tutorial classes. In one semester there were seven tutorials offered at different times in the Decision making unit. Table below provides the number of students who selected each of the seven tutorial classes:

Tutorial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | Total |

No. of Students | 18 | 12 | 25 | 23 | 8 | 19 | 14 | 119 |

Does the data indicate that students have a preference for certain tutorials or do they indicate that each tutorial was equally likely to be chosen? Explain your answer fully. Show all your workings clearly.

#### Question 5:

Suppose you move to another city after graduation to take up a new job. You will, of course, be concerned about the problems you will face commuting to and from work. You would like to know, for example, how long you will it take you to drive to work each morning. Using “one-way distance to work” as a measure of where you live, your employer has collected the following data based on fifteen (15) of the employees in the company. Fifteen of your potential coworkers have given the following data of one-way travel time and distances to work.

Data on Commute Distances and Time

Coworkerl | Distance in Kilometers | Time to travel in minutes |

1 | 3 | 7 |

2 | 5 | 20 |

3 | 7 | 20 |

4 | 8 | 15 |

5 | 10 | 25 |

6 | 11 | 17 |

7 | 12 | 20 |

8 | 12 | 35 |

9 | 13 | 26 |

10 | 15 | 25 |

11 | 15 | 35 |

12 | 16 | 32 |

13 | 18 | 44 |

14 | 19 | 37 |

15 | 20 | 45 |

**a)**Find the line of best fit and the variance of Y about the line of best fit. Explain in your words what do these calculations indicate.

**b)**Find the 95% confidence interval for the population slope.

**c)**Is the line of best fit useful in making a decision that one-way distance is suitable in indicating one-way travel time?

**d)**Construct a 95% confidence interval for the mean travel time for the coworkers who travel 7 Kilometres to work.

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