Picosoft, Ltd., a supplier of operating system software for personal computers, was planning the initial public offering of its stock in order to raise sufficient working capital to finance the development of a radically new, seventh-generation integrated system. With current earnings of $1.61 a share, Picosoft and its underwriters were contemplating an offering price of $21, or about 13 times earnings. In order to check the appropriateness of this price, they randomly chose seven publicly traded software firms and found that their average price/earnings ratio was 11.6, and the sample standard deviation was 1.3. At α = 0.02, can Picosoft conclude that the stocks of publicly traded software firms have an average P/E ratio that is significantly different from 13?
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