Question: A well-known manufacturer of flat screen, HDTV screens is considering changing the width to height ratio on its product. In particular they want to see if the ratio of the dimension of its screens is of importance to the consumer. The marketing department had several different versions of their screens designed with different width to height ratios. Their traditional screen has a ratio of 4: 3. The design changes to increase or decrease the ratio involves nothing more than adding or deleting pixels and rearranging some of them to meet the ratio dimensions, the size of the body that holds the screen would remain essentially unchanged.

The marketing department collected data from a sample of 100 potential customers and ran several tests on the data to help them make suggestions to senior management on a possible change to the screen design. The marketing department had 11 different screen designs made with different ratios and asked the potential customers to respond with some identifying information, and, which design they thought was the most appealing. The results of the sample were categorized in several different ways for their analyses

First, the marketing department was not even sure if there would be a preference for different screen ratios. The sample data was categorized into 5 different ratio groups and if there were no preference they expected to find \(20 \%\) of the potential consumers selecting each of the categories. The following is the data from the sample of 100 potential consumers. At the 0.01 level of significance test to see if the results met their "no preference" expectations or if there was actually a preference for one or more of the screen ratio options. The value of the test statistic for this test was calculated and is given as 22.60.

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