Refer to the IEICE Transactions on Information & Systems (Jan. 2005) comparison of two methods of testing electronic circuits, Exercise 7.52. Each of 11 circuits was tested using the standard compression/depression method and the new Huffman based coding method, and the compression ratio recorded. The data are reproduced in the accompanying table. In theory, the Huffman coding method will yield a smaller mean compression ratio.
a. Test the theory using α = .05.
b. Does your conclusion, part a, agree with the inference derived from the 95% confidence interval found in Exercise 7.52?

Data from Exercise 7.52

Japanese researchers have developed a compression/depression method of testing electronic circuits based on Huffman coding. (IEICE Transactions on Information & Systems, Jan. 2005.) The new method is designed to reduce the time required for input decompression and output compression—called the compression ratio. Experimental results were obtained by testing a sample of 11 benchmark circuits (all of different sizes) from a SUN Blade 1000 workstation. Each circuit was tested using the standard compression/depression method and the new Huffman-based coding method, and the compression ratio was recorded.

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CIRCUITS Circuit Standard Method Huffman Coding Method 1 .80 .78 2 .80 .80 3 .83 .86 4 .53 .53 .50 .51 .96 .68 99 .82 8. .98 .72 9 .81 45 10 .95 .79 11 .99 .77 67