. Some of the customers in each café were given survey forms to complete to find out if they were satisfied with the standard of service they received. Pete s Eats Alan s Diner Sarah s Snackbar Total Dissatisfied 6 8 6 40 Satisfied 6 0 4 80 Total 4 8 50 0 One of the survey forms was chosen at random, find the probability that the form showed Dissatisfied ; the form showed Satisfied and was completed at Sarah s Snackbar; the form showed Dissatisfied, given that it was completed at Alan s Diner. A χ test at the 5 % significance level was carried out to determine whether there was any difference in the level of customer satisfaction in each of the cafés. (d) Write down the null hypothesis, H 0, for the χ test. Write down the number of degrees of freedom for the test. Using your graphic display calculator, find calc. (g) State, giving a reason, the conclusion to the test. (Total marks) IB Questionbank Mathematical Studies rd edition
. A manufacturer claims that fertilizer has an effect on the height of rice plants. He measures the height of fertilized and unfertilized plants. The results are given in the following table. Plant height Fertilized plants Unfertilized plants > 75 cm 5 80 50 75 cm 45 65 < 50 cm 0 5 A chi-squared test is performed to decide if the manufacturer s claim is justified at the % level of significance. Write down the null and alternate hypotheses for this test. For the number of fertilized plants with height greater than 75 cm, show that the expected value is 97.5. () Write down the value of calc. (d) Write down the number of degrees of freedom. Write down the critical value of χ, at the % level of significance. Is the manufacturer s claim justified? Give a reason for your answer. (Total marks) IB Questionbank Mathematical Studies rd edition
. It is thought that the breaststroke time for 00 m depends on the length of the arm of the swimmer. Eight students swim 00 m breaststroke. Their times (y) in seconds and arm lengths (x) in cm are shown in the table below. Length of arm, x cm Breaststroke, y seconds 4 5 6 7 8 79 74 7 70 77 7 64 69 5. 5.7 9. 4.0.8 7.0 5.9 44.0 Calculate the mean and standard deviation of x and y. Given that s xy = 4.8, calculate the correlation coefficient, r. Comment on your value for r. (d) Calculate the equation of the regression line of y on x. () Using your regression line, estimate how many seconds it will take a student with an arm length of 75 cm to swim the 00 m breaststroke. (Total marks) 5. A random sample of 67 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) 0 t 5 5 t 0 0 t 45 45 t 60 60 t 75 75 t 90 Number of people 5 4 7 State the modal group. 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. () On graph paper, draw a fully labelled histogram to represent the data. (Total 8 marks) IB Questionbank Mathematical Studies rd edition
4. The heights and weights of 0 students selected at random are shown in the table below. Student 4 5 6 7 8 9 0 Height x cm 55 6 7 50 8 65 70 85 75 45 Weight y kg 50 75 80 46 8 79 64 9 74 08 Plot this information on a scatter graph. Use a scale of cm to represent 0 cm on the x-axis and cm to represent 0 kg on the y-axis. Calculate the mean height. Calculate the mean weight. (d) It is given that S xy = 44.. (iii) By first calculating the standard deviation of the heights, correct to two decimal places, show that the gradient of the line of regression of y on x is 0.76. Calculate the equation of the line of best fit. Draw the line of best fit on your graph. (6) Use your line to estimate the weight of a student of height 90 cm; the height of a student of weight 7 kg. It is decided to remove the data for student number 0 from all calculations. Explain briefly what effect this will have on the line of best fit. (Total 5 marks) IB Questionbank Mathematical Studies rd edition 4
6. Neil has three dogs. Two are brown and one is grey. When he feeds the dogs, Neil uses three bowls and gives them out randomly. There are two red bowls and one yellow bowl. This information is shown on the tree diagram below. Red Brown Yellow Grey Red Yellow One of the dogs is chosen at random. Find P (the dog is grey and has the yellow bowl). Find P (the dog does not get the yellow bowl). () Neil often takes the dogs to the park after they have eaten. He has noticed that the grey dog plays with a stick for a quarter of the time and both brown dogs play with sticks for half of the time. This information is shown on the tree diagram below. Stick Brown Grey No stick Stick No stick Copy the tree diagram and add the four missing probability values on the branches that refer to playing with a stick. During a trip to the park, one of the dogs is chosen at random. (iii) (iv) Find P (the dog is grey or is playing with a stick, but not both). Find P (the dog is grey given that the dog is playing with a stick). Find P (the dog is grey and was fed from the yellow bowl and is not playing with a stick). (9) (Total marks) IB Questionbank Mathematical Studies rd edition 5