1.A manufacturer of boxed hair dyes, sold in supermarkets, claims that about 0.5% of all users will have an allergic reaction to their products. This manufacturer produces approximately 6000 boxes of hair dye per day during business hours, 5 days per week. A consumer group has received several complaints from users of this product who suffered allergic reactions. The consumer group has approached the manufacturer, asking for a response. The manager was asked to randomly sample some boxed hair dyes to test for correct chemical ingredients. After selecting a random sample of 10 boxes of hair dyes, and testing, the manager found 1% of boxed hair dyes had incorrect chemical ingredients that could lead to an allergic reaction in a user. 10 Please answer each of the following, in the context of this question. ?a)Describe the "Who" and "Why" of the data. ?b)What is the value of the statistic and what is the value of the parameter? c) Will the sample collected by the manager suffer from any sampling error? If so, briefly explain your answer and how it may be remedied.

2.The wine industry in Australia is based on vineyards. The department of agriculture wants to explore the size of vineyards (acres) in South Australia and took a random sample with the following results: 420, 150, 250, 360, 150, 230 a) Calculate the mean, median and mode of the data. ?Using your answers from part a), what is the shape of the distribution of the data set? Briefly explain. ?Calculate and interpret the coefficient of variation of the data. Show basic workings.

3.A store analyzed a sample of its recent sales and recorded the value of the sale and the method of payment. The results are summarized in the following table:

Size of purchase Method of payment Under $20 $20 to $100 Over $100 Total Cash 65 73 87 225 Credit card 15 33 120 168 Debit card 10 35 62 107 Total 90 141 269 500Here is a frequency table of weekly rental ($) paid by students: Class ($) Frequency (0, 100] 13 (100, 200] 85 (200, 300] 44 (300, 400] 77 (400, 500] 96 How many students paid more than $100 per week in rent but less than or equal to $400 per week