The table showing the stock price changes for a sample of 12 companies on a day is contained in the Excel file below.

Price Change ($)
0.82
1.44
-0.07
0.41
0.21
1.33
0.97
0.30
0.14
0.12
0.42
0.15

Construct a spreadsheet to answer the following questions.
a. Compute the sample variance for the daily price change (to 4 decimals).
b. Compute the sample standard deviation for the price change (to 4 decimals).
c. Provide 95% confidence interval estimates of the population variance (to 4 decimals).

(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 X  denote the stock price changes for a sample of 12 companies on a day.

The data provided is:

X = {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 - α)% confidence interval for population variance is:

Compute the critical value of Chi-square for α = 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).

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step-by-step explanation:

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