5 /A class took a mathematics test (marked out of 80) and an English test (marked out of 100), and the results are given in the following table. Maths 15 25 37 45 60 72 74 78 78 79 79 English 44 47 42 49 52 44 54 59 69 78 89 a Calculate the PMCC for this data and comment on the result. Use graphing software to plot these points on a scatter diagram and comment on your result from a. c Calculate Spearman's rank correlation coefficient for this data and comment on your result. d State which is the more valid measure of correlation, and give a reason.4 A sports scientist is testing the relationship between the speed of muscle movement and the force produced. In 10 tests the following data is collected. 35 OD 30 K B -25 C 20 Force (N/kg) D 15 E- F I 10 5 0 -0.5 015 1 15 2 2.5 30 3.5 4 -- 5 Velocity (m/s) Point . A = (0.25, 30.4) . E = (1.52, 13.4) . 1 = (2.93, 10.8) . B = (0.51, 25.1) . F = (2.02, 13.4) . J = (3.17, 10.3) . C = (0.69, 20) . G - (2.43, 11.2) . K = (-0.29, 25.07) . D = (1.09, 15.6) . H = (2.67, 10.2) . L = (3.09, -2.44) a Explain why it might not be appropriate to use the PMCC in this case. b Calculate Spearman's rank correlation coefficient (r ) for this data. C Interpret the value of r, and comment on its validity. 3852 A survey was conducted to find out which type of bread males and females prefer. Eighty people were interviewed outside a baker's shop and the results are shown below. Bread White Brown Corn Multi- Totals grain Male 14 10 8 39 Female 17 6 6 12 41 Totals 31 16 13 20 80 Using the x2 test at the 5% significance level, determine whether the favourite type of bread is independent of gender. a State the null hypothesis and the alternative hypothesis. b Show that the expected frequency for female and white bread is approximately 17.9. c Write down the number of degrees of freedom. d Write down the x2 test statistic and the p-value for this data. The critical value is 7.815. e Comment on your result.2 There are 60 students in Grade 12. Mr Stewart asks them which month their birthdays are in, and the results are shown in the table. Month Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Frequency 3 5 4 6 5 6 4 8 6 3 3 The months in which people have birthdays are uniformly distributed.a Write down the table of expected values. b Write down the number of degrees of freedom. c Determine the results of a goodness of fit test at the 10% significance level to find out whether the data fits a uniform distribution. Remember to write down the null and alternative hypotheses. The critical value for this test is 17.275. d State the conclusion for the test and give a reason for your answerExercise 8D 1 Terri buys 10 packets of Skittles and counts a Find the expected frequencies. how many of each colour (yellow, orange, b Write down the number of degrees of red, purple and green) there are. In total freedom. she has 600 sweets. c Determine the results of a goodness of fit According to the Skittles website, the test at the 5% significance level to find colours should be evenly distributed with out whether Terri's data fits a uniform 20% of each colour in a bag. distribution. Remember to write down The results for Terri's 10 bags are: the null and alternative hypotheses. The critical value for this test is 9.488. Colour Frequency d State the conclusion for the test and give Yellow 104 a reason for your answer. Orange 132 Red 98 Purple 129 Green 137Exercise 8E Marius works in a fish shop. One week he he decides to perform a x2 goodness of fit measures 250 fish before selling them. His test at the 5% significance level to find out results are shown in the table. whether the fish that he measured could Length of fish, x cm Frequency have come from a population with this distribution. 9Ex