Calculate a confidence interval for the population, Basic Statistics

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A Shoe manufacturing company designs a new shoe (Brand A) and it wanted to compare its fit with that of the leading brands in the market Nike and Reebok. 27 Customers were asked to try one of the brands and rate its comfort which was measured on 1 (bad) to 9 (good) scales. The new shoe will be introduced only if it is preferred over the other 2 brands. The scores are given below:

              Nike                       Reebok                      Brand A

                7                              4                              3

                5                              6                              5

                8                              7                              8

                7                              8                              5

                5                              4                              9

                6                              6                              7

                8                              3                              8

                5                              7                              5

                7                              6                              6

 

                H (1): Is Brand A preferred over Nike?

                H (2): Is Brand A preferred over Reebok?

The CEO of supermarket 'Taste' thinks of opening a branch in another shopping mall in Hong Kong. But before that he wants to study the consumer's preference for a particular store based on the variety of items sold in that store. He would compare his store with the leading supermarket chains like PNS and Welcome in a study in which 30 consumers participate. They are given a questionnaire which listed the variety of products sold in a particular departmental store for different item categories and asked them to rate their preference for that store which was measured on a 10 pointer scale, 1 (less preferred) and 10 (more preferred). These are then averaged for a single consumer and are given below in a table.

             PNS                        Welcome                     Taste

                3                              4                              6

                4                              6                              7

                6                              5                              4

                7                              4                              8

                8                              3                              9

                9                              6                              4

                6                              8                              5

                7                              6                              4

                6                              4                              7

                5                              8                              7

The CEO will open a branch only if consumers prefer 'Taste' departmental store over PNS and Welcome. What will be his decision?


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