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1. A company inspector monitors the number of items in) produced each week together with the production costs (pi. The results are shown in this table: Number of items 27 75 78 12 15 (niin 10005 Production costs 42 91 37 73 (pi in 10005 Use your calculator to: a) Calculate the value of the product moment correlation coefficient for these data. Write your answer to 4 significant gu res (2) b) Write down the equation of the regression line of n on p in the form p = a + ha. (2) c) Does the value of the correlation coefficient support the use of a linear regression model? Write a sentence to explain your answer. (1) 2. Soojin owns a restaurant. She records the weekly sales figures in pounds (f), and the average number of customers for 12 weeks. The product moment correlation coefficient for these data is 0.5427 a) Stating your hypotheses clearly and using a one tailed test with a 5% level of significance, test whether or not the correlation between sales figures and number of customers is positive. (3) b) If the significance level is changed to 2.5%, would the result of the hypothesis test be the same? Explain why. (1) c) Suggest a possible reason why the conclusions in parts a and b might be different.3. Two restaurant critics rank eight chefs in a cooking competition. The results are shown in this table. Chef Critic 1 rank Critic 2 rank A 3 2 B 2 5 C 6 W D UT J E F 4 G H 8 6 (a) Calculate the Spearman rank correlation coefficient (rs) between the two critics. Use the table to record your calculations. (5) (b) One of the chefs wants to test the hypothesis that there is positive correlation between the ranks of the two critics. (i) Write down the critical value for the correlation coefficient at the 5% level. (1) (ii) Does your value for rs support the hypothesis? Give a reason for your answer and interpret the result. (2)