Complete the equationof the line whose slope is -2 and y-intercept is (0,-8)

The authors of a paper describe an experiment to evaluate the effect of using a cell phone on reaction time. Subjects were asked

Serggg [28]

Answer:

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

b) n=464

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".

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)

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

$df=n-1=47-1=46$

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(0.025,46)".And we see that $t_{\alpha/2}=2.01$

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

$525-2.01\frac{75}{\sqrt{47}}=503.01$

$525+2.01\frac{75}{\sqrt{47}}=546.99$

So on this case the 95% confidence interval would be given by (503.01;546.99)

Part b

The margin of error is given by this formula:

$ME=t_{\alpha/2}\frac{s}{\sqrt{n}}$ (1)

And on this case we have that ME =7 msec, we are interested in order to find the value of n, if we solve n from equation (1) we got:

$n=(\frac{t_{\alpha/2} s}{ME})^2$ (2)

The critical value for 95% of confidence interval is provided, $t_{\alpha/2}=2.01$ from part a, replacing into formula (2) we got:

$n=(\frac{2.01(75)}{7})^2 =463.79 \approx 464$

So the answer for this case would be n=464 rounded up to the nearest integer

8 0

3 years ago

What is the equation, in standard form, of a parabola that models the values in the table?

Vitek1552 [10]

Answer:

b. 4x^2 + 3x - 6

Step-by-step explanation:

The values of f(x) for the extremes of x are more positive than the value of f(x) for the middle x, so we know the parabola opens upward. That eliminates choice D.

It is probably easiest to evaluate the other expressions to see which one matches the given f(x) values. For the purpose, it is usually easier to use the Horner form of the equation.

a. f(-2) = (3(-2) +4)(-2) -6 = -2(-2) -6 = -2 ≠ 4

b. f(-2) = (4(-2) +3)(-2) -6 = -5(-2) -6 = 4 . . . . matches the given data point

c. Because (b) matches, we know this one will not.

The appropriate choice is B.