0.08 or 0.8 Bigger or smaller or is 0.08 bigger or less than 0.8

Marine biologists have been studying the effects of acidification of the oceans on weights of male baluga whales in the Arctic O

oksano4ka [1.4K]

Answer:

a) 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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

And the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And replacing we got:

$ME=1.96\frac{125}{\sqrt{16}}=61.25$

b) $ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =45 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

$n=(\frac{1.960(125)}{45})^2 =29.64 \approx 30$

So the answer for this case would be n=30 rounded up to the nearest integer

b. 30

c) And for this case the conditions in order to use the confidence interval are satisfied since:

a. Yes. The distribution of sample means is normal because the data are normal.

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".

$\bar X$ represent the sample mean for the sample

$\mu$ population mean (variable of interest)

$\sigma =125$ represent the population standard deviation

n=16 represent the sample size

Part a

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 tabel to find the critical value. The excel command would be: "=-NORM.INV(0.025,0,1)".And we see that $t_{\alpha/2}=1.96$

And the margin of error is given by:

$ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}$

And replacing we got:

$ME=1.96\frac{125}{\sqrt{16}}=61.25$

c. 61.25 kg

Part b

The margin of error is given by this formula:

$ME=z_{\alpha/2}\frac{s}{\sqrt{n}}$ (a)

And on this case we have that ME =45 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

$n=(\frac{z_{\alpha/2} \sigma}{ME})^2$ (b)

$n=(\frac{1.960(125)}{45})^2 =29.64 \approx 30$

So the answer for this case would be n=30 rounded up to the nearest integer

b. 30

Part c

And for this case the conditions in order to use the confidence interval are satisfied since:

a. Yes. The distribution of sample means is normal because the data are normal.

7 0

3 years ago

Solve: 7m + 12 = −4m + 78

Mandarinka [93]

7m + 12 = -4m + 78

7m + 4m = 78 - 12

11m = 66

m = 6

I hope you understand...

Mark me as brainliest...

7 0

3 years ago

What is the volume of a cube on which each face has a diagonal of 12.8 inches? (round to nearest tenth)

Aleksandr-060686 [28]

Answer:

volume of cube = side^3

=12.8^3

=2097. 152

7 0

3 years ago

Read 2 more answers

HELP HELP HELPH EPLHEPLHEPLHEPLHEPLEP

Soloha48 [4]

Answers:

1a) y=-10/3x+90

1b) 20

1c) -18

2a) 2.8

2b) How much the heights of five basketball players vary from the average height.

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Explanations:

1a) The trend line is linear, so we just need to find the slope and y-intercept to find an equation for it. Our y-intercept is (0,90), or 90, and our slope is -10/3. Our equation is now y=-10/3x+90.

1b) To find when x=21, we plug 21 into our equation where the x is. Now we do the math.

y=-10/3(21)+90 (plug in)

y=-70+90 (simplify by multiplying -10/3 by 21)

y=20 (simplify by adding -70 to 90)

Therefore, we can predict that when x is 21, y is 20.

1c) To find when y=150, we plug 150 into our equation where the y is. Now we do some more math.

150=-10/3x+90 (plug in)

60=-10/3x (subtract 90 from both sides

-18=x (divide both sides by -10/3)

Therefore, we can predict that when y is 150, x is -18.

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2a) The mean absolute deviation (or MAD for short) of a data set is calculated as such:

Step 1) Find the mean (average) by finding the sum of the data values, then dividing the sum of the data values by the number of data values. In this case, we have the numbers 65, 58, 64, 61, and 67, which add up to 315. The data set has 5 numbers, so we divide our sum of 315 by 5 to get 63. Therefore, our mean is 63.

Step 2) Find the absolute value of the distance between each data value and the mean. In this case, we find out how far away each data value is from 63, our mean. To do this, we subtract 63 from each number.

65-63=2

58-63=-5

64-63=1

61-63=-2

67-63=4

Some of these values are negative, but we're using absolute value so they all become positive. We now have a new set of values: 2, 5, 1, 2, and 4.

Step 3) Finally, we calculate the mean of our new set of values. In this case, we will add up 2, 5, 1, 2, and 4 to get 14 and divide by 5 to get our MAD of 2.8. Therefore, the MAD (and the answer to problem 2a) is 2.8.

2b) Now we just find out what the MAD means in this context. The MAD always is a measure of variance in a data set. In this context, it's describing how much the heights (in inches) of five people on a basketball team vary from the average height.

Hope this helps!

3 0

3 years ago

How to round to the naerst 10?

Blababa [14]

So, say your # was 6,234,578. you would go to the seven and look to the number next to in, so 8, and if the neighbor is 5 or bigger, you make the number, in this case a 7 an 8. Last, you make all the other #s after the one you rounded 0. So the answer would be:

6,234,570.0

3 0

3 years ago