Visits Purchases 9 4 15 6 6 4 13 9 15 5 6 2 6 5 6 6 15 4 14 8 8 5 10 11 11 8 15

Question

Visits Purchases 9 4 15 6 6 4 13 9 15 5 6 2 6 5 6 6 15 4 14 8 8 5 10 11 11 8 15 5 13 10 8 6 12 7 9 6 8 7 5 1 11 7 7 4 5 1 9 5 15 5 15 6 14 9 6 5 12 4 5 1 7 5 14 8 11 8 10 6 6 3 13 12 7 7 6 5 13 4 6 5 11 6 8 7 10 6 8 0 12 3 10 6 6 3 5 2 14 10 13 4 The dataset in the file Shopping. csv linked below reports information for an "approached in-store at random" sample of 50 of a store's customers. For each sampled customer, both the number of store visits and number of items purchased last year are recorded. The store management is interested in estimating the number of items purchased per customer last year. As you can verify, the average number of items purchased last year amongst the sampled customers is 5.52. However, you are concerned that the nature of the sampling is such that frequent customers are over-represented in the sample. To deal with this, you assume that the probability of "catching" a specific customer in the sample is proportional to his/her number of store visits. Using this assumption, give a better estimate of the target than 5.52. Report your answer to two decimal places.

Explanation / Answer

Here as the probability of "catching' a specific customer in the sampe of proporrtional to his/her number of store visits.

so now we will get the value of purchase * probability of visit.

Here probability of visit = Number of visit by a perticulat person/ Total visit by 50 person.

The data is compiled in the given table.

Here sum of total visit = 493

so probability of viist by a specific customer = i/ 493

so total visit = purchase by that customer * (vist by this customer /493)

that we will take sum of it.

so, the better estimate would be 5.96

Visits Purchases Purchase per visit 9 4 0.0730 15 6 0.1826 6 4 0.0487 13 9 0.2373 15 5 0.1521 6 2 0.0243 6 5 0.0609 6 6 0.0730 15 4 0.1217 14 8 0.2272 8 5 0.0811 10 11 0.2231 11 8 0.1785 15 5 0.1521 13 10 0.2637 8 6 0.0974 12 7 0.1704 9 6 0.1095 8 7 0.1136 5 1 0.0101 11 7 0.1562 7 4 0.0568 5 1 0.0101 9 5 0.0913 15 5 0.1521 15 6 0.1826 14 9 0.2556 6 5 0.0609 12 4 0.0974 5 1 0.0101 7 5 0.0710 14 8 0.2272 11 8 0.1785 10 6 0.1217 6 3 0.0365 13 12 0.3164 7 7 0.0994 6 5 0.0609 13 4 0.1055 6 5 0.0609 11 6 0.1339 8 7 0.1136 10 6 0.1217 8 0 0.0000 12 3 0.0730 10 6 0.1217 6 3 0.0365 5 2 0.0203 14 10 0.2840 13 4 0.1055 493 5.52 5.9615

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