A random sample of 51 of the largest companies in the united states gave the following P/e ratios
11 35 19 13 15 21 40 18 60 72 9 20
29 53 16 26 21 14 21 27 10 12 47 14
33 14 18 17 20 19 13 25 23 27 5 16
8 49 44 20 27 8 19 12 31 67 51 26
19 18 32
Use a calculator with mean and sample standard deviation keys to verify that xbar = 25.2 and s=15.5
find a 99 % confidence interval for the P/E population mean of all large companies
Bank One merged with JP morgan had a P/E of 12, AT7t had a P/E of 72 Disney had a P/E of 24 Examine the confidence intervals in b and c how would you describe the stocks at the time the sample was taken
To verify the values of x-bar (sample mean) and s (sample standard deviation), you can use a calculator with mean and sample standard deviation keys. Follow these steps:
1. Input the given data into the calculator: 11, 35, 19, 13, 15, 21, 40, 18, 60, 72, 9, 20, 29, 53, 16, 26, 21, 14, 21, 27, 10, 12, 47, 14, 33, 14, 18, 17, 20, 19, 13, 25, 23, 27, 5, 16, 8, 49, 44, 20, 27, 8, 19, 12, 31, 67, 51, 26, 19, 18, 32.
2. Calculate the mean (x-bar) using the mean key on the calculator.
mean = (11 + 35 + 19 + 13 + 15 + 21 + 40 + 18 + 60 + 72 + 9 + 20 + 29 + 53 + 16 + 26 + 21 + 14 + 21 + 27 + 10 + 12 + 47 + 14 + 33 + 14 + 18 + 17 + 20 + 19 + 13 + 25 + 23 + 27 + 5 + 16 + 8 + 49 + 44 + 20 + 27 + 8 + 19 + 12 + 31 + 67 + 51 + 26 + 19 + 18 + 32) / 51
3. Calculate the sample standard deviation (s) using the sample standard deviation key on the calculator.
4. Verify that the calculated values match the given values x-bar = 25.2 and s = 15.5.
To find a 99% confidence interval for the P/E population mean of all large companies, you can follow these steps:
1. Calculate the margin of error (E) using the formula: E = critical value * (s / sqrt(n)), where n is the sample size.
2. Determine the critical value for a 99% confidence level. A z-score table or a calculator with a built-in z-score function can be used to find the z-score. The z-score for a 99% confidence level is approximately 2.576.
3. Substitute the values into the formula for the margin of error (E): E = 2.576 * (15.5 / sqrt(51)).
4. Calculate the lower bound of the confidence interval: lower bound = x-bar - E.
5. Calculate the upper bound of the confidence interval: upper bound = x-bar + E.
The resulting confidence interval will be in the form (lower bound, upper bound).