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3 years ago

In the problems below, f(x) = log2x and

Mathematics

1 answer:

Varvara68 [4.7K]3 years ago

8 0

Answer:

dc better and more grown up than that marvel craap

Step-by-step explanation:

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Suppose that the researchers wanted to estimate the mean reaction time to within 6 msec with 95% confidence. Using the sample st

Lisa [10]

Answer:

a) The 95% confidence interval would be given by (509.592;550.308)

b) n=523 rounded up to the nearest integer

Step-by-step explanation:

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".

$\bar X=530$ represent the sample mean for the sample

$\mu$ population mean

s=70 represent the sample standard deviation

n=48 represent the sample size (variable of interest)

Confidence =95% or 0.995

Part a

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

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

The degrees of freedom are df=n-1=48-1=47

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: "=-T.INV(0.025,47)".And we see that $z_{\alpha/2}=2.01$

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

$530-2.01\frac{70}{\sqrt{48}}=509.692$

$530+2.01\frac{70}{\sqrt{48}}=550.308$

So on this case the 95% confidence interval would be given by (509.592;550.308)

Part b

The margin of error is given by this formula:

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

Assuming that $\hat \sigma =s$

And on this case we have that ME =6msec, 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)

The critical value for 95% of confidence interval is provided, $z_{\alpha/2}=1.96$ , replacing into formula (b) we got:

$n=(\frac{1.96(70)}{6})^2 =522.88 \approx 523$

So the answer for this case would be n=523 rounded up to the nearest integer

3 0

3 years ago

What is the answer for |x|-7=8 <br> A) x=1<br> B) x= 15<br> C)x= -1 or 1<br> D) x= -15 or 15

borishaifa [10]

The answer is D. "x=-15 or 15."

You can solve this by adding seven on both sides.
|x|-7=8
+7 +7
------------
|x|=15

Therefore, x is either equal to 15 or -15.

8 0

3 years ago

The elevation of city A is 72 feet above sea level; the elevation of City C is 24 feet above sea level. The elevation of city D

emmasim [6.3K]

Answer:

Step-by-step explanation:

Given that elevation of the cities are

A=72 feet

C=24 feet

D=1/4 of C

The expression for the elevation of city D is

D=C/4

substituting C=24 in the expression we have

D=24/4

D=6

The answer is positive because the elevation is above sea level

7 0

4 years ago

What multiple of 10 is 78 closest to?<br><br> So 78 rounds to

ludmilkaskok [199]

Answer:

Step-by-step explanation:

78 is only 2 from 80 while it is 8 from 70

3 0

3 years ago

Read 2 more answers

A bank PIN is a string of four digits, each digit 0-9. (a) How many choices are there for a PIN if the last digit must be odd? M

Amanda [17]

Answer:

a) 5,000 b) 3,600

Step-by-step explanation:

a) there are four different slots, and for the first three slots there are a possibility for 10 different numbers and in the last slot there can only be 5 different numbers. So you get 10 x 10 x 10 x 5 which leaves you with 5,000 possibilities

b) the same thing as above but know you have fewer numbers 10 x 9 x 8 x5 which gives you 3,600 possibilities

7 0

4 years ago