The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, and others) gave the following P/E ratios.† 24 16 22 14...

The price to earnings ratio (P/E) is an important tool in financial work. A random sample of 14 large U.S. banks (J. P. Morgan, Bank of America, and others) gave the following P/E ratios.†

The sample mean is

Generally speaking, a low P/E ratio indicates a "value" or bargain stock. Suppose a recent copy of a magazine indicated that the P/E ratio of a certain stock index is μ = 19. Let
x
be a random variable representing the P/E ratio of all large U.S. bank stocks. We assume that
x
has a normal distribution and σ = 5.5. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use α = 0.01.