## Investigations Exercise

1. a. To simulate the weekly draw of Lotto use the string of random digits below to pick seven random numbers from 1 to 40.

You may start at any position in the string.

 3 2 3 8 8 9 1 8 3 9 0 2 7 4 2 3 6 5 7 8 3 4 6 2 5 4 5 6 6 7 5 3 1 8 6 0 9 0 5 6

b. Select seven numbers for the Lotto game using the RND# button on your calculator.

c. Select the seven numbers using a computer spreadsheet.

2. In a secondary school, the Principal wants to find out the students' opinion of the new gymnasium. She wants to have a sample of 50 students spread across the year levels. There are 850 students at the school and the numbers in each form is given in the table below. Complete the table below to find how many students are needed from each level for a stratified sample.

 Year Level Number of students % of total roll Number of students in sample* Year 8 150 Year 9 180 Year 10 200 Year 11 180 Year 12 140

* rounded to nearest whole number.

3. State whether the following methods would generate a random and unbiased sample

 a. At the Olympic Games every athlete who wins a bronze medal is selected for drug testing b. To predict the result of a general election every 10th person on the main street of a city at lunch time is asked who they will vote for. c. To select 6 people from a group of 40, number the people from 1 to 40 and use the first six numbers from the weekend Lotto draw. d. To find out customers opinions about home telephone services, Telecom asks every 200th person in the telephone directory's white pages.

4. A survey is being held to find out how students at a secondary school of 1000, travel to school.
Which of the following methods would produce a random sample of size 50.
Give a reason for each answer and state whether you think the results would be biased.

a. You go to the main entrance of the school at 8.30 am and ask the first 50 people who come through the gate.

b. You go to the front office and get an alphabetical list of all of the students at the school and pick every 20th student from the list.

c. You phone every tenth person on the list in the evening.

d. You go to the Year 12 assembly and ask 50 students their views.

 5 A computer software company wants to find out which of the features of one of its programs people like the best. They e-mail 100 of the people who have bought the program and filled in the registration form and ask them questions. Would this method give unbiased results?

6. Which of the following methods of selecting a random sample of 50 adults from Wellington would produce the best results? You want to ask them if they enjoy living in Wellington. Give a reason for your answers.

a. Going to the stadium for a Super 12 rugby game and choosing 50 people.

b. Choosing the first 50 people in the Melbourne or Wellington telephone directory.

c. Picking out an office building in central Canberra and asking the first 50 people coming out after work.

d. Select the first 50 people from the voters' roll for Brisbane.