Mathematics, 08.11.2019 01:31 thomasgnathan

Asimple random sample from a population with a normal distribution of 106106 body temperatures has x overbarxequals=98.1098.10degrees upper f°f and sequals=0.610.61degrees upper f°f. construct anan 8080% confidence interval estimate of the standard deviation of body temperature of all healthy humans.

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Using the chi-square distribution, the 80% confidence interval estimate of the standard deviation of body temperature of all healthy humans is (0.5477, 0.6856).

The sample size is n = 106

The significance level is $\alpha = 1 - 0.8 = 0.2$

The estimate, which is the sample standard deviation, is of s = 0.61 .

Now, we have to find the critical values for the chi-square distribution. They are:

$\chi^2_{\frac{\alpha}{2},n-1} = \chi^2_{0.05,105} = 129.92$

$\chi^2_{1-\frac{\alpha}{2},n-1} = \chi^2_{0.95,105} = 82.35$

The confidence interval for the population variance is:

$\frac{(n-1)s^2}{\chi^2_{\frac{\alpha}{2},n-1}} < \sigma^2 < \frac{(n-1)s^2}{\chi^2_{1-\frac{\alpha}{2},n-1}}$

$\frac{105(0.61)^2}{129.92} < \sigma^2 < \frac{105(0.61)^2}{82.35}$

$0.3 < \sigma^2 < 0.47$

The standard deviation is the square root of the variance, thus:

$\sqrt{0.3} = 0.5477, \sqrt{0.47} = 0.6856$ .

The 80% confidence interval estimate of the standard deviation of body temperature of all healthy humans is (0.5477, 0.6856).

A similar problem is given at link

Answer from: jakails359

(97.084, 99.116)

Step-by-step explanation:

As per given , we have

sample size :n= 106

degree of freedom: df = 105 (df=n-1)

$\overline{x}=98.10\\ s=0.61$

Significance interval : $\alpha: 1-0.80=0.20$

Since , population standard deviation is unknown , so we use t-test .

Using t-value table ,

$t_{df,\ \alpha/2}=t_{(105,\ 0.10)}=1.290$

Now , 80% Confidence interval will be :

$\overline{x}\pm t_{df,\ \alpha/2}\dfrac{s}{\sqrt{n}}$

$98.10\pm (1.290)\dfrac{0.61}{\sqrt{0.6}}$

$\approx98.10\pm 1.016$

$=(98.10- 1.016,\ 98.10+ 1.016)=(97.084,\ 99.116)$

Thus , The 80% confidence interval estimate of the standard deviation of body temperature of all healthy humans = (97.084, 99.116).

Answer from: Quest

Answer: choice c and choice d

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explanation

the graph has a slope of 1/3 because each time you move up 1, you go to the right 3. so, slope = rise/run = 1/3. we can cross choice a off the list since we want a slope of 3, rather than 1/3.

the first table shown has a slope of -3. this is because the rise is -6 and the run is 2, so slope = rise/run = -6/2 = -3. note how x increases by 2 each time (run) and y drops by 6 each time (rise). choice b can be eliminated.

the second table has a slope of 3. each time x goes up by 1, the y values increase by 3. slope = rise/run = 3/1 = 3. alternatively you can use the slope formula to prove that the slope is 3 here. use any two rows of values to generate the two points. choice c is one of the answers

the third table also has a slope of 3. let's use the slope formula to prove as such. i'm going to use the first two rows of the table. so i'll use the two points (2,1) and (5,10)

m = slope

m = (y2-y1)/(x2-x1)

m = (10-1)/(5-2)

m = 9/3

m = 3 so we get a slope of 3

choice d is the other answer

Which functions have an additive rate of change of 3? check all that apply

Answer from: Quest

the correct answer is a) they believe they have a "just cause."

islamic terrorists justify their violent actions because they believe they have a "just cause."

every act of terrorism of islamic sects is done “in the name of allah”. that justifies their actions. islam people who commit those terrorist attacks are not afraid to die. that is why the attacks have horrible consequences. they know they are going to die and they are proud to do it because it is in the name of allah, so it is justified and is for a “good cause.”

since the very beginning of the conflict with israel, islam is fighting a “sacred war”, respecting the words stated in the qur’an. they fight against the domination of the western countries and to defend their occupied territories.