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VMariaS [17]
3 years ago
11

Allen's hummingbird (Selasphorus sasin) has been studied by zoologist Bill Alther.â  Suppose a small group of 11 Allen's humming

birds has been under study in Arizona. The average weight for these birds is x = 3.15 grams. Based on previous studies, we can assume that the weights of Allen's hummingbirds have a normal distribution, with Ï = 0.38 gram.
Find an 80% confidence interval for the average weight of Allen's hummingbirds in the study region. What is the margin of error?
Mathematics
1 answer:
alexira [117]3 years ago
8 0

Answer:

3.15-1.28\frac{0.38}{\sqrt{11}}=3.003    

3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297    

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147    

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=3.15 represent the sample mean

\mu population mean (variable of interest)

\sigma=0.38 represent the population standard deviation

n=11 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 0.80 or 80%, the value of \alpha=0.2 and \alpha/2 =0.1, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-NOR.INV(0.1,0,1)".And we see that z_{\alpha/2}=1.28

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

3.15-1.28\frac{0.38}{\sqrt{11}}=3.003    

3.15+ 1.28\frac{0.38}{\sqrt{11}}=3.297    

So on this case the 80% confidence interval would be given by (3.003;3.297)

And the margin of error is given by:

ME = 1.28\frac{0.38}{\sqrt{11}}= 0.147    

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Answer:

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Step-by-step explanation:

Given that p is at the distance of 3/4 from A to B

it mean that point p divides the line AB into 3:4 ratio.

and

if there are two points (x1,y1) and (x2,y22) which is divided by point p in the ratio m:n then

coordinates of point p (x,y) is given

p (x = (n*x1+m*x2)/m+n , y = (n*y1+m*y2)/m+n )

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Given the points AB

A(2,5)

B(6,9)

m:n = 3:4

thus,

p (x = (4*2+3*6)/7 , y = (4*5+3*9)/7 )

p (x = (4*2+3*6)/7 , y = (4*5+3*9)/7 )

p (x = (26/7 , y = 47/7 )

P ( x = 3.71, y = 6.71)

Thus, coordinates of point p  is (3.71, 6.71) which is  at  3/4 of the distance from A to B for A(2,5) and B(6,9)/

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Find the equation for the trend line through the points (0, 11) and (100, 33). Then use it to predict the number of baskets Romy
sleet_krkn [62]

Answer:

28 baskets

Step-by-step explanation:

The equation for a linear trend line is given by:

y = mx + b, where y and x are variables, m is the slope of the line and b is the y intercept (that is value of y when x is zero).

The equation of a line passing through two points (x_1,y_1)\ and\ (x_2,y_2) is:

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y represent the number of baskets made and x represents the time take. Given that the line passes through the points  (0, 11) and (100, 33), hence:

y-11=\frac{33-11}{100-0}(x-0)\\\\y-11=\frac{11}{50}x\\\\y=  \frac{11}{50}x+11

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y=\frac{11}{50}x+11\\\\y=\frac{11}{50}(80)+11  \\\\y=17.6+11\\\\y=28.6\\\\Therefore\ y\ =\ 28\ baskets

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