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
Find the mean first = sum of scores/number of scores
Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.
Standard deviation = square root of variance
90% = mean ± 2.575 SD
I'll let you do the calculations.
I'm not clear on what you are asking for in the last part.
To find the sample mean (x̄) and sample standard deviation (s), you need to input the given data into a calculator with mean and sample standard deviation keys. Here's how you can find x̄ and s:
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. Use the mean key on the calculator to find x̄ (the sample mean). The result should be x̄ = 25.2.
3. Use the sample standard deviation key on the calculator to find s (the sample standard deviation). The result should be s = 15.5.
Now, to find the 99% confidence interval for the P/E population mean of all large companies, you can use the following formula:
CI = x̄ ± z * (s / √n)
Where:
CI = Confidence Interval
x̄ = Sample Mean
z = Z-score for the desired level of confidence (99% in this case)
s = Sample Standard Deviation
n = Sample Size
To find the Z-score for a 99% confidence level, you can consult a Z-score table or use a calculator with a built-in Z-score function. The Z-score for a 99% confidence level is approximately 2.576.
Substituting the values into the formula:
CI = 25.2 ± 2.576 * (15.5 / √51)
Calculating the values:
CI = 25.2 ± 2.576 * (15.5 / 7.141)
CI = 25.2 ± 5.66
This gives you the confidence interval as (19.54, 30.86).
Now, let's consider the given P/E ratios of Bank One (12), AT&T (72), and Disney (24) and examine their positions within the confidence interval:
- Bank One (12) falls below the lower bound of the confidence interval (19.54), indicating that its P/E ratio is significantly lower than the estimated population mean at the time the sample was taken.
- AT&T (72) falls above the upper bound of the confidence interval (30.86), suggesting that its P/E ratio is significantly higher than the estimated population mean at the time the sample was taken.
- Disney (24) falls within the confidence interval, indicating that its P/E ratio is not significantly different from the estimated population mean at the time the sample was taken.
In summary, based on the confidence intervals, Bank One had a relatively low P/E ratio, AT&T had a relatively high P/E ratio, and Disney had a P/E ratio that was consistent with the estimated population mean at the time the sample was taken.