Mathematics, 04.12.2019 06:31 amandapill

Anew species of sea crab has been discovered, and an experiment conducted to determine whether or not the animal can regulate its temperature. that the animal can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability. ten of these sea crabs were exposed to ambient temperatures of 24 degrees celsius. their body temperatures were measured with the results below: 24.33, 24.61, 24.67, 24.64, 24.42, 24.97, 25.23, 24.73, 24.90, 24.44for purposes of this example, assume that it is reasonable to regard these 10 crabs as a random sample from the population of all crabs of this species. a)- calculate a point estimate of the population mean. b)-construct and interpret a 99% confidence interval for m. c)-does it appear from these data that the crabs are able to regulate their body temperature? provide statistical justification for your response.

Answers: 2

Show answers

Answers

Answer from: oneicyahdaley10

a) $\hat \mu =\bar X=24.694$

b) The 99% confidence interval would be given by (24.409;24.979)

c) Since the 99% confidence interval not contains the exposed to ambient temperatures of 24 degrees Celsius, and since the animals "that can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability", on this case we can conclude that the sea crabs are able to regulate their body temperature.

Step-by-step explanation:

1) 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".

Data: 24.33, 24.61, 24.67, 24.64, 24.42, 24.97, 25.23, 24.73, 24.90, 24.44

$\bar X$ represent the sample mean

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=10 represent the sample size

Part a

A point of estimate for the population mean is the sample mean, given by this formula:

$\bar X= \frac{\sum_{i=1}^n x_i}{n}$

If we apply this formula we got that $\hat \mu =\bar X=24.694$

Part b

In order to calculate the confidence interval first we need to calculate the sample deviation given by this formula:

$s=\frac{\sum_{i=1}^n (x_i -\bar x)}{n-1}$

If we use this formula we got that s=0.277

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

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

In order to calculate the critical value $t_{\alpha/2}$ we need to find first the degrees of freedom, given by:

df=n-1=10-1=9

Since the Confidence is 0.99 or 99%, the value of $\alpha=0.01$ and $\alpha/2 =0.005$ , and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,9)".And we see that $t_{\alpha/2}=3.25$

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

$24.694-3.25\frac{0.277}{\sqrt{10}}=24.409$

$24.694+3.25\frac{0.277}{\sqrt{10}}=24.979$

So on this case the 99% confidence interval would be given by (24.409;24.979)

Part c

Since the 99% confidence interval not contains the exposed to ambient temperatures of 24 degrees Celsius, and since the animals "that can maintain a body temperature different from the surroundings would be considered evidence of this regulating capability", on this case we can conclude that the sea crabs are able to regulate their body temperature.

Answer from: Quest

your exact question is kind of difficult to understand, so maybe an example will explain what you're supposed to do? i'll work through the first problem on the worksheet.

suppose you have a tray of 652 brownies, and you have 5 friends that you want to feed without picking favorites. how many brownies can you dole out to each of your friends in equal amounts? how many will be left over for you to eat?

what you're doing here is finding a way to arrange the number 652 as the sum of integer multiple of 5 and some remainder: $652=5q+r$

here $q$ ("q" for quotient) is the number of brownies each of your friends get, and $r$ is the remainder. that's the basic idea behind division.

we break up the number 652 into parts so that the leading digit stands on its own:

652 = 600 + 52

first we check if it's possible to hand out exactly 100 brownies to each friend. with 5 friends, this means we want to know if we can take out 500 brownies from the tray. we can do this 1 time because we have 600 brownies to take from, and when we do that we're left with 100 + 52 brownies to divvy up. so we know that

652 = 1*500 + 152

next we want to know if it's possible to hand out exactly 10 brownies per friend. if we can, we have to remove 50 brownies from the tray each time until we can't. we have 152 brownies left, and we know that 3(50) = 150, so

152 = 3*50 + 2

now we have 2 brownies left in the tray. is it possible to hand 1 out to each of your 5 friends? no, you'd need a minimum of 5 brownies to do that. so the last 2 are yours.

putting everything together, we found that

652 = 1*500 + 3*50 + 2

and we can rearrange this to write

652 = 5*100 + 5*30 + 2

652 = 5(100 + 30) + 2

652 = 5*130 + 2

so $q=130$ and $r=2$ .

you might be more accustomed to the table depicting the algorithm. that's just a compact way of organizing what we've done above. you can consult the image i've attached below.

Answer from: Quest

The answer would be c 0.02