Solve the proportion 2/43 = j/13

The percentage of body fat of a random sample of 36 men aged 20 to 29 found a sample mean of 14.42. Find a 95% confidence interv

Rina8888 [55]

Answer:

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

Step-by-step explanation:

Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

$\bar X=14.42$ represent the sample mean

$\mu$ population mean (variable of interest)

$\sigma=6.95$ represent the population standard deviation

n=36 represent the sample size

Solution to the problem

The confidence interval for the mean is given by the following formula:

$\bar X \pm z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$ (1)

Since the Confidence is 0.95 or 95%, the value of $\alpha=0.05$ and $\alpha/2 =0.025$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $z_{\alpha/2}=1.96$

Now we have everything in order to replace into formula (1):

$14.42-1.96\frac{6.95}{\sqrt{36}}=12.150$

$14.42+ 1.96\frac{6.95}{\sqrt{36}}=16.690$

So on this case the 95% confidence interval would be given by (12.150;16.690)

5 0

3 years ago

Solve the system of equations using elimination 2x+y=3 and 3x-y=12

Eddi Din [679]

2x + y = 3
3x - y = 12
Add both equations
5x = 15, x = 3
2(3) + y = 3
6 + y = 3, y = -3
Solution: x = 3, y = -3... or (3,-3)

3 0

3 years ago

PLEASE HELPPPPPPPP ASAAAAP1!!!!!!!!

Radda [10]

As far as I can tell, that isn't a function at all.

x = 0 produces y = -2 and y = 4, which can't happen.

Please don't use all caps, that's really, really irritating.

3 0

3 years ago

If x / 3 equals 6 then x equals

sleet_krkn [62]

Answer: X = 18

Step-by-step explanation:

Crossmultiply

8 0

3 years ago

Find sin theta if cot theta = -2 and cos theta < 0

Katarina [22]

cot(θ) = cos(θ)/sin(θ)

So if both cot(θ) and cos(θ) are negative, that means sin(θ) must be positive.

Recall that

cot²(θ) + 1 = csc²(θ) = 1/sin²(θ)

so that

sin²(θ) = 1/(cot²(θ) + 1)

sin(θ) = 1 / √(cot²(θ) + 1)

Plug in cot(θ) = -2 and solve for sin(θ) :

sin(θ) = 1 / √((-2)² + 1)

sin(θ) = 1/√(5)

6 0

2 years ago