Blockbusters Statistics Rules of the Game n n

Blockbusters!!! Statistics

Rules of the Game n n n Two teams play against each other to make it across the board before the other team. Team 1 asks for a number. The teacher will click on that number. Team 1 answers the question. If they are right, that block belongs to Team 1 and is colored in with Team 1’s color. If they are wrong, they do not get the block and it is now Team 2’s turn. Each team is trying to get across the board while also blocking the other team’s progress. The first team to make it to the other side wins.

Choose a Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

1 The table below shows the frequency distribution of the number of dental fillings for a group of 25 children. n n Number of fillings 0 1 2 3 4 5 Frequency 4 3 8 q 4 1 (a) Find the value of q. (b) Use your graphic display calculator to find (i) the mean number of fillings; (ii) the median number of fillings; (iii) the standard deviation of the number of fillings.

2 56 students were given a test out of 40 marks. The teacher used the following box and whisker plot to represent the marks of the students. n n (a) Write down (i) the median mark; (ii) the 75 th percentile mark; (iii) the range of marks. (b) Estimate the number of students who achieved a mark greater than 32.

3 Oral tests are conducted by three examiners A, B and C separately. The results of the examination are classified as Credit, Pass or Fail. A χ2 test is applied to the data collected in order to test whether or not the examiners differ in their standard of awards. n (a) State the null hypothesis, H 0, for this data. n (b) Write down the number of degrees of freedom. Of the 135 students who sit the exam, 30 get Credit and 45 are tested by examiner A. n (c) Calculate the expected number of students who get a Credit and are tested by examiner A. Using a 5% level of significance, the p-value is found to be 0. 0327 correct to 3 s. f. n (d) State whether H 0 should be accepted. Justify your answer.

4 80 matches were played in a football tournament. The following table shows the number of goals scored in all matches. Number of goals 0 1 2 3 4 5 Number of matches 16 22 19 17 1 5 (a) Find the mean number of goals scored per match. n (b) Find the median number of goals scored per match. A local newspaper claims that the mean number of goals scored per match is two. n (c) Calculate the percentage error in the local newspaper’s claim. n

5 A market researcher consulted males and females to determine whether the type of coffee they drink is associated with gender. The types of coffee are Cappuccino, Latte, Americano, Macchiato and Espresso. A χ2 test was conducted, at the 5 % significance level, and the χ2 value was found to be 8. 73. n (a) Write down (i) the null hypothesis; (ii) the alternative hypothesis. n (b) Write down the number of degrees of freedom for this test. n (c) Write down the critical value for this test. n (d) State whether the type of coffee drunk is independent of gender. Give a reason for your answer.

6 The following stem and leaf diagram gives the weights in kg of 34 eight year-old children. Key: 26│1 reads 26. 1 kg n n n (a) The median weight is 30. 3 kg. Find the value of t. (b) Write down the lower quartile weight. (c) The value of the upper quartile is 31. 6 kg and there are no outliers. Draw a box and whisker plot of the data using the axis below.

7 The following table shows the number of errors per page in a 100 page document. n n Number of errors 0 1 2 3 4 Number of pages 28 24 20 17 11 (a) State whether the data is discrete, continuous or neither. (b) Find the mean number of errors per page. (c) Find the median number of errors per page. (d) Write down the mode.

8 The birth weights, in kilograms, of 27 babies are given in the diagram below. Calculate the mean birth weight. n Write down: (i) the median weight; (ii) the upper quartile. The lower quartile is 2. 3 kg. n (c) On the scale below draw a box and whisker diagram to represent the birth weights. n (a) (b)

9 31 pupils in a class were asked to estimate the number of sweets in a jar. The following stem and leaf diagram gives their estimates. n (a) For the pupils’ estimates, write down (i) the median; (ii) the lower quartile; (iii) the upper quartile. n (b) Draw a box and whisker plot of the pupils’ estimates using the grid below.

10 Tom performs a chi-squared test to see if there is any association between the time to prepare for a penalty kick (short time, medium time and long time) and the outcome (scores a goal, doesn’t score a goal). Tom performs this test at the 10% level. n (a) Write down the null hypothesis. n (b) Find the number of degrees of freedom for this test. n (c) The p-value for this test is 0. 073. What conclusion can Tom make? Justify your answer.

11 The heights (cm) of seedlings in a sample are shown below. n n (a) (b) (c) (d) State how many seedlings are in the sample. Write down the values of (i) the median; (ii) the first and third quartile. Calculate the range. Using the scale below, draw a box and whisker plot for this data.

12 Eight houses in a street are inhabited by different numbers of people, as shown in the table below. House A B C D E F G H Number of inhabitants 5 4 7 6 4 3 6 4 (a) The following statements refer to the number of inhabitants per house. Write down true (T) or false (F) for each. (i) The mean is 5. (ii) The range is 4. (iii) The mode is 6. (iv) The standard deviation is 1. 4 correct to 2 significant figures. n (b) Calculate the interquartile range for the number of inhabitants per house. n

13 The distribution of the weights, correct to the nearest kilogram, of the members of a football club is shown in the following table. Weight (kg) Frequency 40 – 49 6 50 – 59 18 60 – 69 14 70 – 79 4 n (a) On the grid below draw a histogram to show the above weight distribution. n (b) (c) (d) n n Write down the mid-interval value for the 40 – 49 interval. Find an estimate of the mean weight of the members of the club. Write down an estimate of the standard deviation of their weights.

14 A random sample of 167 people who own mobile phones was used to collect data on the amount of time they spent per day using their phones. The results are displayed in the table below. Time spent per day (t minutes) Number of people n n n 0 <= t <15 15 <= t < 30 30 <= t < 45 45 <= t < 60 60 <= t < 75 75 <= t < 90 21 32 35 41 27 11 (a) State the modal group. (b) Use your graphic display calculator to calculate approximate values of the mean and standard deviation of the time spent per day on these mobile phones. (c) On graph paper, draw a fully labelled histogram to represent the data.

15 The number of hours that a professional footballer trains each day in the month of June is represented in the following histogram. n (a) Write down the modal number of hours trained each day. n (b) Calculate the mean number of hours he trains each day.

16 A researcher consulted 500 men and women to see if the colour of the car they drove was independent of gender. The colours were red, green, blue, black and silver. A test was conducted at the 5% significance level and the value found to be 8. 73. n (a) Write down the null hypothesis. n (b) Find the number of degrees of freedom for this test. n (c) Write down the critical value for this test. n (d) Is car colour independent of gender? Give a clear reason for your answer