Mathematics, 05.05.2020 17:04 anishivaturi123

Here are the weights, in pounds, of a sample of 13 adult female golden retriever dogs: 59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4. what are the degrees of freedom, and what's the critical value of t needed to construct a 95% confidence interval for the population mean weight of adult female golden retrievers?

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95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].

Step-by-step explanation:

We are given that the weights, in pounds, of a sample of 13 adult female golden retriever dogs :

59.0, 54.1, 53.7, 51.6, 57.5, 58.7, 58.0, 53.8, 48.9, 53.9, 51.6, 55.9, and 57.4.

Firstly, the pivotal quantity for 95% confidence interval for the population mean is given by;

P.Q. = $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ ~ t_n_-_1

where, $\bar X$ = sample mean weight = $\frac{\sum X }{n}$ = 54.9 pounds

s = sample standard deviation = $\frac{\sum (X-\bar X)^{2} }{n-1}$ = 3.12 pounds

n = sample of female = 13

$\mu$ = population mean weight

Here for constructing 95% confidence interval we have used One-sample t test statistics because we don't know about population standard deviation.

So, 95% confidence interval for the population mean, $\mu$ is ;

P(-2.179 < t_1_2 < 2.179) = 0.95 {As the critical value of t at 12 degree

of freedom are -2.179 & 2.179 with P = 2.5%}

P(-2.179 < $\frac{\bar X -\mu}{\frac{s}{\sqrt{n} } }$ < 2.179) = 0.95

P( $-2.179 \times {\frac{s}{\sqrt{n} } }$ < ${\bar X -\mu}$ < $2.179 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

P( $\bar X-2.179 \times {\frac{s}{\sqrt{n} } }$ < $\mu$ < $\bar X +2.179 \times {\frac{s}{\sqrt{n} } }$ ) = 0.95

95% confidence interval for $\mu$ = $\bar X \pm 2.179 \times {\frac{s}{\sqrt{n} } }$

= [ $54.9 - 2.179 \times {\frac{3.12}{\sqrt{13} } }$ , $54.9 +2.179 \times {\frac{3.12}{\sqrt{13} } }$ ]

= [53.01 pounds , 56.78 pounds]

Therefore, 95% confidence interval for the population mean weight of adult female golden retrievers is [53.01 pounds , 56.78 pounds].

Answer from: Quest

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be). so point b is at (-2,2). point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

Answer from: Quest

765238725478629038640962136509762139056074

step-by-step explanation:

64087235609746097215074621039754021037

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Here are the weights, in pounds, of a sample of 13 adult female golden retriever dogs: 59.0, 54.1, 5...

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