# Assessment Item

**Assessment Item 2—Assignment 2**

Due date: | 5:00pm, Friday, Week 10 | ASSESSMENT |

Weighting: | 20% | 2 |

Length: | One file (.doc, .docx) no more than 15 MB |

## Assessment criteria

- This assignment must be typed, word-processed or clearly hand-written
**(but plots and graphs must be done using EXCEL or equivalent software),**and submitted online as a single file through Moodle.**Important Note:**The file size must not be over 100MB. - Microsoft Excel allows students to cut and paste information easily into Microsoft Word documents. Word also allows the use of Microsoft Equation Editor to produce all necessary formulae (use of these are recommended).
- It is expected that Excel would be used to assist in statistical calculations for questions in this assignment. Where Excel is used, use copy function, “Snipping tool” or similar to cut and paste relevant parts of the spreadsheet to verify that you have done the work. (In that case there is no need to write the equations.)
- For those questions where Excel is not used to do the computations, all formulae and working must be included to obtain full marks.
- Only one file will be accepted in the formats mentioned above. No zipped file or any other file extension will be accepted. Also,
**no submission as an email attachment will be accepted**. - There will be
**late submission penalty**for submissions beyond the deadline unless prior approval is obtained from the Unit Coordinator through the extension system in Moodle. Submissions 14 days or more after the deadline will receive a score of zero.

Assignment markers will be looking for answers which

and*Demonstrate the student’s ability to interpret and apply the statistical techniques in the scenarios*.*Use statistical techniques as decision making tools in the business environment*

Full marks will not be awarded to answers which simply demonstrate statistical procedures without comment, interpretation, or discussion (as directed in the questions).

## Plagiarism

CQU values academic honesty. Consequently, plagiarism will not be tolerated in assessment items. This assignment must be completed by each student individually.

**(a)**The table below shows the age of customers who purchased a new phone plan from a telecom company. Construct a stem and leaf plot for the data.**1.5 marks**

53 | 55 | 20 | 42 | 40 |

28 | 41 | 63 | 46 | 23 |

58 | 67 | 27 | 60 | 59 |

31 | 34 | 44 | 54 | 53 |

50 | 33 | 61 | 34 | 61 |

32 | 47 | 53 | 53 | 45 |

- Construct a frequency distribution for the data provided below using “20 to less than 30” as the first class. Approximate the sample mean and standard deviation from the frequency distribution.

**1.5 marks**

Bin | Frequency |

20 | 4 |

30 | 5 |

40 | 7 |

50 | 9 |

60 | 5 |

- Draw a relative frequency histogram using the data above.
**1 mark**

The following table provides product survey results for the reliability rating of four mobile phone brands. A value of 0 represents completely unreliable and a value of 100 indicates completely reliable. Using the data in the table answer the following questions.

Reliability Scores for Mobile Phone Brands | |||

Brand A | Brand B | Brand C | Brand D |

77 | 85 | 50 | 50 |

65 | 89 | 39 | 89 |

79 | 46 | 95 | 57 |

45 | 75 | 68 | 54 |

83 | 81 | 33 | 60 |

68 | 78 | 37 | 69 |

65 | 61 | 72 | 82 |

43 | 74 | 73 | 62 |

53 | 56 | 70 | 92 |

66 | 63 | 30 | 64 |

- Compute the mean, median, first quartile, and third quartile for each brand.

Use the exact position, (n+1)f, where n is the number of observations and f is the relevant fraction for the quartile. **1**** ****mark**

- Calulate the standard deviation, range and coefficient of variation from the data for each brand.
**1 mark**

- Draw a box and whisker plot for the reliability of each brand and put them side by side on the same scale so that the reliability of the phones can be compared.
**1 mark**

- Compare the box plots and comment on the distribution of the data.
**1 mark**

Players in a football league were surveyed using a simple random sample to find their performance in relation to the amount of training they do through the week.

Training (hours/week) | ||||||

Performance | 0 | 1-5 | 5-10 | > 10 | Total | |

Low | 5 | 8 | 20 | 2 | 35 | |

Medium | 1 | 30 | 27 | 18 | 76 | |

High | 1 | 15 | 21 | 35 | 72 | |

Total | 7 | 53 | 68 | 55 | 183 |

If a player is chosen randomly from the league, answer the following questions based on the data in the table:

- What is the probability that a player is training through the week?
**1 mark**

- What is the probability that a player that trains more that ten hours per week will only achieve medium performance?
**1 mark**

- What is the probability that a player will practice for 5 or more hours per week?
**1 mark**

- What is the probability that a player will not train are will be a low performer?
**1 mark**

- (a) A car company collected data and found that their brake pads lasted for a mean distance of 180 thousand kilometers with a standard deviation of 20 thousand kilometers. The data was found to be normally distributed. The supplier of the brake pads had specified the lifetime of the brake pads to be 150 thousand kilometers.

- What percentage of brake pads will under perform?
**1 Mark**

- The car company has decided to specify the percentage of brake pads that under perform to 1%. What should the standard deviation need to be to meet this requirement?
**1 mark**

- The annual income of car company workers on the production line was found to have a mean of

$35,000 and a standard deviation of $6,000. If random samples of 50 production line workers were taken from the production line, calculate the proportion of sample mean annual incomes that would exceed $37,500. **1 mark**

- The number of years of service of 10 car company production line workers varies uniformly between 5 years and 12.5 years. What is the probability that the length of employment for a production line worker is 10 years?
**1 mark**

- The Department of Education found that only 55 percent of students attend school in a remote community. If a random sample of 500 children is selected, what is the approximate probability that at least 250 children will attend school? Use normal approximation of the binomial distribution.
**1.5 marks**

- A hotel chain found that 120 out of 225 visitor who booked a room cancelled their bookings prior to the 24hr no refund period. Determine whether there is evidence that the population proportion of visitors who book their stay and cancel their bookings prior to the no refund period is less than 50% at a 1% confidence level.
**1.5 marks**

- The Queensland education department surveyed 1000 parents to assess those with having financial hardship. It was determined that 19% of the parents suffered some financial hardship of which 10% could not afford the full cost of their childs education. Construct a 99% confidence interval for the proportion of parents who are suffering financial hardhip and cannot afford the full cost of their child’s education.
**1 mark**