3x -7= -5(x+3); x= -1

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

AfilCa [17]

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 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:

$s^{2}=\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}$

The sample mean is computed using the formula:

$\bar X=\frac{1}{n}\sum\limits^{12}_{i=1}{X_{i}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample mean and sample variance are:

$\bar X$ =AVERAGE(A2:A13)

$s^{2}$ =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:

$s=\sqrt{\frac{1}{n-1}\sum\limits^{12}_{i=1}{(X_{i}-\bar X)^{2}}}$

Consider the Excel output attached below.

In Excel the formula to compute the sample standard deviation is:

$s$ =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:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

Compute the critical value of Chi-square for α = 0.05 and (n - 1) = (12 - 1) = 11 degrees of freedom as follows:

$\chi^{2}_{\alpha/2, (n-1)}=\chi^{2}_{0.05/2,11}=21.920$

$\chi^{2}_{1-\alpha/2, (n-1)}=\chi^{2}_{(1-0.05/2),11}=\chi^{2}_{0.975,11}=3.816$

*Use a Chi-square table.

Compute the 95% confidence interval estimates of the population variance as follows:

$CI=[\frac{(n-1)s^{2}}{\chi^{2}_{\alpha/2} } \leq \sigma^{2}\leq \frac{(n-1)s^{2}}{\chi^{2}_{1-\alpha/2} } ]$

$=[\frac{(12-1)\times 0.2501}{21.920 } \leq \sigma^{2}\leq \frac{(12-1)\times 0.2501}{3.816} ]$

$=[0.125506\leq \sigma^{2}\leq 0.720938]\\\approx [0.1255, 0.7210]$

Thus, the 95% confidence interval estimates of the population variance is (0.1255, 0.7210).

7 0

4 years ago

Not the best pic but I think it’s still readable.. pls answer for all.. thanks

luda_lava [24]

Answer:

a) y=5ˣ-3

b) y=5ˣ⁻²

c) y=5^(x+1/2)

d) y=5^(x+2.5)+1

Step-by-step explanation:

$y=b*5^{ax-h}+k$

b: vertical stretch or compression and reflection across x-axis

a: horizontal stretch or compression and reflection across y-axis

h: horizontal shift (left and right)

k: vertical shift (up and down)

a) y=5ˣ-3

b) y=5ˣ⁻²

c) y=5^(x+1/2)

d) y=5^(x+2.5)+1

5 0

3 years ago

32 pages in 4 days = pages per day

KatRina [158]

Answer:

8 páginas al día para leer

8 0

3 years ago

Which of the following options is an equivalent function to f(x) = 4(3)2X?

Paha777 [63]

Answer:

$f(x)=4(6x)$

Step-by-step explanation:

Given:

the given expression is.

$f(x)=4(3)2x$

Simplify the given expression.

$f(x)=4(3)2x$

$f(x)=4(3\times 2x)$

$f(x)=4(6x)$

Therefore, the option $f(x)=4(6x)$ is an equivalent function to $f(x)=4(3)2x$ .

8 0

3 years ago

Calculate the value of the following: sin 120+tan 300 <img src="https://tex.z-dn.net/?f=sin%20120%20%2B%20tan%20300" i

Korolek [52]

Answer: 45.825353255

Step-by-step explanation:

5 0

3 years ago

3x -7= -5(x+3); x= -1​

3x -7= -5(x+3); x= -1