What is 0.37 (7repeating) as a fraction
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Answer:
(a) The sample variance for the daily price change is 0.2501.
(b) The sample standard deviation for the daily price change is 0.5001.
(c) The 95% confidence interval estimates of the population variance is (0.1255, 0.7210).
Step-by-step explanation:
Let the random variable <em>X</em> denote the stock price changes for a sample of 12 companies on a day.
The data provided is:
<em>X</em> = {0.82 , 1.44 , -0.07 , 0.41 , 0.21 , 1.33 , 0.97 , 0.30 , 0.14 , 0.12 , 0.42 , 0.15}
(a)
The formula to compute the sample variance for the daily price change is:
The sample mean is computed using the formula:
Consider the Excel output attached below.
In Excel the formula to compute the sample mean and sample variance are:
=AVERAGE(A2:A13)
=VAR.S(A2:A13)
Thus, the sample variance for the daily price change is 0.2501.
(b)
The formula to compute the sample standard deviation for the daily price change is:
Consider the Excel output attached below.
In Excel the formula to compute the sample standard deviation is:
=STDEV.S(A2:A13)
Thus, the sample standard deviation for the daily price change is 0.5001.
(c)
The (1 - <em>α</em>)% confidence interval for population variance is:
Compute the critical value of Chi-square for <em>α</em> = 0.05 and (n - 1) = (12 - 1) = 11 degrees of freedom as follows:
*Use a Chi-square table.
Compute the 95% confidence interval estimates of the population variance as follows:
Thus, the 95% confidence interval estimates of the population variance is (0.1255, 0.7210).
