A manufacturing firm is planning the initial public offering of its stock in order to raise sufficient capital to finance a new plant. With current earnings of $1.61 a share, the firm and its underwriters are 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 manufacturing firms and found that their average price/earnings ratio was 11.6, and the sample standard deviation was 1.3. At an alpha of .02, can the firm conclude that the stocks of publicly traded manufacturing firms have an average price/earnings ratio that is significantly different from 13?

Question

A manufacturing firm is planning the initial public offering of its stock in order to raise sufficient capital to finance a new plant. With current earnings of $1.61 a share, the firm and its underwriters are 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 manufacturing firms and found that their average price/earnings ratio was 11.6, and the sample standard deviation was 1.3. At an alpha of .02, can the firm conclude that the stocks of publicly traded manufacturing firms have an average price/earnings ratio that is significantly different from 13?

Answer 1

You can use a one-sample z-test.

z = (sample mean - population mean)/(standard deviation divided by the square root of the sample size)

With your data:
z = (11.6 - 13)/(1.3/√7) = ?

Finish the calculation.

If you use an alpha of .02 for a two-tailed test, then the cutoff or critical value from a z-table would be ±2.33. Does your test statistic exceed either the plus critical value or the minus critical value? If it does, then you can conclude a significant difference.

I hope this will get you started.