SECTION C: SAMPLING AND CONFIDENCE INTERVALS Question C1 [3 marks] The manager of 'Care-Full' wants to select a random sample of 4 employees from his workforce of 10 Care Workers. He first assigns each Care Worker a random number (to 2 d.p.) as shown in the table below Name Staff Number H.Amla 101 S.Bates L.Patel H.Lara B.Obama V.Kholi 102 103 104 105 106 P.Conti 107 H.Wells Q.Zhang G.Kruis 108 109 110 Random 0.08 0.86 0.22 0.84 0.41 0.29 0.51 0.78 0.28 0.59 1) Using the 'Random Sampling Method 2' outlined in the lecture, what is the staff number of the third Care Worker chosen for the sample? 2) Decide whether the following statement is true (enter1), false (enter 2) or it is not possible to tell (enter 3). "For the sampling method used in part 1), each employee from the workforce had an equal chance of being selected." 3) Which one of the following Excel functions (with answers rounded to 2 decimal places) could be used to generate the random numbers in the table above? ⚫ =RANDOM() (Enter 1) • =RANDOM (0.01, 0.99) • =RAND() (Enter 2) (Enter 3) • =RAND(0,1) (Enter 4) =RANDBETWEEN (0.01, 0.99) (Enter 5) Question C2 [2 marks] A haulage company employs 132 drivers, 36 office workers and 72 mechanics. A manager selects a sample of 20 employees using random stratified sampling. 1) How many drivers are selected? 2) What percentage of the sample of 20 employees are mechanics? 1, 2, 3, 4 or 5 to 1dp Enter Staff Number Enter 1, 2 or 3/nQuestion C3 [2 marks] A Quality Control Manager takes a systematic sample of size 5 from a total of 30 components. 1) Calculate the sampling interval to be used. 2) Suppose a random number of 5 is generated to start the sampling process. If the components are numbered 1 to 30, state the number of the 3rd component selected in the sample. Question C4 [3 marks] A recruitment agency has four offices with five employees in each office as shown in the table below Office 1 Office 2 Office 3 Random Number: 0.97 Random Number: 0.07 Random Random Number: 0.52 Office 4 Random Number: 0.31 RandomIT Employee | Staff No. | Random No. | Employee Staff No. P. Abu 11 0.83 D.Abbott 21 0.73 31 0.88 Employee Staff No. Random No. Employee |Staff No. M.Gove V.Cable 41 0.74 J. Baker 12 0.56 A.Rayner 22 0.66 B.Johnson 32 0.49 E.Davey 42 0.46 H. Lu 13 0.09 K.Starmer 23 0.28 Y.E. Shin 14 0.86 G. Yates 15 0.29 E.Miliband D.Lammy 24 25 0.33 0.24 P.Patel G.Shapps 34 E.Truss 33 35 0.19 0.08 0.27 L.Moran J.Swinson C.Umunna 43 0.64 44 0.78 45 0.27 The Managing Director of the agency wants to select a working party of 4 employees using multi-stage cluster sampling (using the same procedure as given in the lecture slides). Using the offices as clusters, the Managing Director assigns each office a random number as shown in the table. Two offices are chosen for sampling. 1) State the Office Number of the first of the offices chosen for sampling. Each employee has been assigned a random number and two employees from each of the chosen offices are selected using Random Sampling. 2) State the Staff Number of the first employee chosen from the office stated in Part 1) 3) State the Staff Number of the first employee chosen from the other office chosen for sampling. Enter 1, 2, 3 or 4 Enter Staff Number Enter Staff Number/n5 Question C5 [1 mark] Decide whether you think the following statements are TRUE or FALSE. 5 7 B 9 1 2 B 7 5 5 First "Quota Sampling is not a random sampling method." Second "Using a Snowball Sampling method will ensure the organiser of a survey chooses a sample which is representative of the target group." If you think: First Second then Enter TRUE TRUE 1 TRUE FALSE 2 FALSE TRUE 3 FALSE FALSE 4 (1, 2, 3 or 4) B Question C6 [2 marks] 9 , A random sample of 150 kitchen cabinets are measured and the mean length is found to be 747 mm with a standard deviation of 4.6 mm. Find an 80% confidence interval for the mean cabinet length. 1 2 1) Lower limit of the confidence interval to 2 dp B 7 2) Upper limit of the confidence interval to 2 dp 5 5 7 3.

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