Answer:
The 95% confidence interval for the population variance is ![\left[0.219, \hspace{0.1cm} 0.807\right]\\\\](https://tex.z-dn.net/?f=%5Cleft%5B0.219%2C%20%5Chspace%7B0.1cm%7D%200.807%5Cright%5D%5C%5C%5C%5C)
The 95% confidence interval for the population mean is ![\left [15.112, \hspace{0.3cm}15.688\right]](https://tex.z-dn.net/?f=%5Cleft%20%5B15.112%2C%20%5Chspace%7B0.3cm%7D15.688%5Cright%5D)
Step-by-step explanation:
To solve this problem, a confidence interval of 
for the population variance will be calculated.
Then, the confidence interval for the population variance is given by:
![\left [\frac{(n-1)S^2}{\chi^2_{\left (\frac{\alpha}{2};n-1\right )}}, \hspace{0.3cm}\frac{(n-1)S^2}{\chi^2_{\left (1-\frac{\alpha}{2};n-1\right )}} \right ]\\\\](https://tex.z-dn.net/?f=%5Cleft%20%5B%5Cfrac%7B%28n-1%29S%5E2%7D%7B%5Cchi%5E2_%7B%5Cleft%20%28%5Cfrac%7B%5Calpha%7D%7B2%7D%3Bn-1%5Cright%20%29%7D%7D%2C%20%5Chspace%7B0.3cm%7D%5Cfrac%7B%28n-1%29S%5E2%7D%7B%5Cchi%5E2_%7B%5Cleft%20%281-%5Cfrac%7B%5Calpha%7D%7B2%7D%3Bn-1%5Cright%20%29%7D%7D%20%5Cright%20%5D%5C%5C%5C%5C)
Thus, the 95% confidence interval for the population variance is:![\\\\\left [\frac{(19-1)(0.6152)^2}{32.852}, \hspace{0.1cm}\frac{(19-1)(0.6152)^2}{8.907} \right ]=\left[0.219, \hspace{0.1cm} 0.807\right]\\\\](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5Cleft%20%5B%5Cfrac%7B%2819-1%29%280.6152%29%5E2%7D%7B32.852%7D%2C%20%5Chspace%7B0.1cm%7D%5Cfrac%7B%2819-1%29%280.6152%29%5E2%7D%7B8.907%7D%20%5Cright%20%5D%3D%5Cleft%5B0.219%2C%20%5Chspace%7B0.1cm%7D%200.807%5Cright%5D%5C%5C%5C%5C)
On other hand,
A confidence interval of for the population mean will be calculated
\![\left[ \bar X - T_{(\alpha/2;n-1}\sqrt{\frac{\S^2}{n}}, \hspace{0.3cm}\bar X + T_{(\alpha/2;n-1}\sqrt{\frac{\S^2}{n}} \right ]\\\\](https://tex.z-dn.net/?f=%5Cleft%5B%20%5Cbar%20X%20-%20T_%7B%28%5Calpha%2F2%3Bn-1%7D%5Csqrt%7B%5Cfrac%7B%5CS%5E2%7D%7Bn%7D%7D%2C%20%5Chspace%7B0.3cm%7D%5Cbar%20X%20%2B%20T_%7B%28%5Calpha%2F2%3Bn-1%7D%5Csqrt%7B%5Cfrac%7B%5CS%5E2%7D%7Bn%7D%7D%20%5Cright%20%5D%5C%5C%5C%5C)
Thus, the 95\% confidence interval for the population mean is:![\\\\\left [15.40 - 2.093\sqrt{\frac{(0.6152)^2}{19}}, \hspace{0.3cm}15.40 + 2.093\sqrt{\frac{(0.6152)^2}{19}} \right ]=\left [15.112, \hspace{0.3cm}15.688\right] \\\\](https://tex.z-dn.net/?f=%5C%5C%5C%5C%5Cleft%20%5B15.40%20-%202.093%5Csqrt%7B%5Cfrac%7B%280.6152%29%5E2%7D%7B19%7D%7D%2C%20%5Chspace%7B0.3cm%7D15.40%20%2B%202.093%5Csqrt%7B%5Cfrac%7B%280.6152%29%5E2%7D%7B19%7D%7D%20%5Cright%20%5D%3D%5Cleft%20%5B15.112%2C%20%5Chspace%7B0.3cm%7D15.688%5Cright%5D%20%5C%5C%5C%5C)
Answer:
A) (4,1) C) (12,3) D) (20,5)
Step-by-step explanation:
Required
Which has a constant of proportionality of 1/4
To solve this, we make use of:
Where k is the constant of proportionality.
Solve for x
<u>Testing the given options</u>
A) (4,1)
B) (8,12)
C) (12,3)
D) (20,5)
E) (12,6)
Answer:
the formulae given do not make sense.
Step-by-step explanation:
Answer:
k pi for k = 0, plus-or-minus 2, plus-or-minus 4, ellipsis
Step-by-step explanation:
The cosine is a maximum when its argument is at multiples of 2π.
k pi for k = 0, plus-or-minus 2, plus-or-minus 4, ellipsis
_____
Both of us could probably read this more easily if you would use appropriate math symbols.
21q^2 bc (7x21) x (q x q)
