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 12 13 17 22 15 19 23 13 11 18 The sample mean is  x ≈ 17.1.  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 = 4.8. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use α = 0.05. (a) What is the level of significance?   State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test?  H0: μ = 19; H1: μ > 19; right-tailedH0: μ = 19; H1: μ < 19; left-tailed    H0: μ ≠ 19; H1: μ = 19; two-tailedH0: μ = 19; H1: μ ≠ 19; two-tailed (b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution.  The Student's t, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The Student's t, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with known σ. Compute the z value of the sample test statistic. (Round your answer to two decimal places.)   Your answer cannot be understood or graded. More Information (c) Find (or estimate) the P-value. (Round your answer to four decimal places.)   Sketch the sampling distribution and show the area corresponding to the P-value.         (d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α?  At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.

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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 12 13 17 22 15 19 23 13 11 18

The sample mean is 

x ≈ 17.1.

 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 = 4.8. Do these data indicate that the P/E ratio of all U.S. bank stocks is less than 19? Use α = 0.05.

(a) What is the level of significance? 
  

State the null and alternate hypotheses. Will you use a left-tailed, right-tailed, or two-tailed test? 
H0: μ = 19; H1: μ > 19; right-tailedH0: μ = 19; H1: μ < 19; left-tailed    H0: μ ≠ 19; H1: μ = 19; two-tailedH0: μ = 19; H1: μ ≠ 19; two-tailed

(b) What sampling distribution will you use? Explain the rationale for your choice of sampling distribution. 
The Student's t, since n is large with unknown σ.The standard normal, since we assume that x has a normal distribution with unknown σ.    The Student's t, since we assume that x has a normal distribution with known σ.The standard normal, since we assume that x has a normal distribution with known σ.

Compute the z value of the sample test statistic. (Round your answer to two decimal places.) 
  Your answer cannot be understood or graded. More Information 

(c) Find (or estimate) the P-value. (Round your answer to four decimal places.) 
  

Sketch the sampling distribution and show the area corresponding to the P-value.
   
   

(d) Based on your answers in parts (a) to (c), will you reject or fail to reject the null hypothesis? Are the data statistically significant at level α? 
At the α = 0.05 level, we reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we reject the null hypothesis and conclude the data are not statistically significant.    At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are statistically significant.At the α = 0.05 level, we fail to reject the null hypothesis and conclude the data are not statistically significant.
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