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 7 public traded software
firms and found that their average price/earnings (P/E) 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?