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A certain test preparation course is designed to help students improve their scores on the MCAT exam. A mock exam is given at the beginning and end of the course to determine the effectiveness of the course. The following measurements are the net change in 6 students' scores on the exam after completing the course: 19, 15, 9, 17, 7, 16. Using these data, construct a 95% confidence interval for the average net change in a students's score after completing the course. Assume the population is approx. normal.Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal placed)Step 4. construct the 95% confidence interval (round answer to 1 decimal place)

Answers

Answer 1

Answer:

Answer:

1) $\bar X =(\sum_(i=1)^n X_i)/(n)=13.8$

2) $s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}=4.8$

3) $t_(\alpha/2)=2.571$

4) The 95% confidence interval would be given by (8.8;18.8)

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".

We can calculate the sample mean and sample deviation with the following formulas:

Step 1. calculate the sample mean for the given sample data (round answer to 1 decimal place)

$\bar X =(\sum_(i=1)^n X_i)/(n)=13.8$

Step 2. Calculate the sample standard deviation for the given sample data ( round answer to 1 decimal place)

$s=\sqrt{(\sum_(i=1)^n (X_i -\bar X)^2)/(n-1)}=4.8$

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

$\mu$ population mean (variable of interest)

s represent the sample standard deviation

n=6 represent the sample size

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

$\bar X \pm t_(\alpha/2)(s)/(√(n))$ (1)

Step 3. Find the critical value that should be used in constructing the confidence interval. ( round answer to 3 decimal places)

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

$df=n-1=6-1=5$

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(0.025,5)".And we see that $t_(\alpha/2)=2.571$

Step 4. construct the 95% confidence interval (round answer to 1 decimal place)

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

$13.8-2.571(4.8)/(√(6))=8.8$

$13.8+2.571(4.8)/(√(6))=18.8$

So on this case the 95% confidence interval would be given by (8.8;18.8)

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What do the factors in the factored form represent?

Answers

Answer:

The factored form tells you the times at which the object's height is zero (the roots). ... Write the equation for this parabola in vertex form, factored form, and general form. From the graph you can see that the x-intercepts are 3 and 5. So the factored form contains the binomial expressions (x 3) and (x 5).

Step-by-step explanation:

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On a coordinate plane, a line goes through (0, negative 3) and (2, 2). A point is at (2, negative 3).Complete the statements about finding the equation of the line that is parallel to line n and passes through point (2, –3).

The slope of the graphed line is
.
The slope of the parallel line is
.
An equation that can be used to find the y-intercept of the parallel line is
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The y-intercept of the parallel line is
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The equation of the parallel line is
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Answers

Answer:

5/2, 5/2, -3= (5/2)(2)+b, -8, y=(5/2)x-8

Step-by-step explanation:

Answer:

The slope of the graphed line is

✔ 5/2

The slope of the parallel line is

✔ 5/2

An equation that can be used to find the y-intercept of the parallel line is

✔ –3 = (5/2)(2) + b

The y-intercept of the parallel line is

✔ –8

The equation of the parallel line is

✔ y = (5/2)x – 8

Step-by-step explanation:

4x<-2 como se desarrolla esta desigualdad

Answers

Answer:

x<-0.5

Step-by-step explanation:

The graph shows the distance, y, that a car traveled in x hours: A graph is shown with the x-axis title as Time in hours. The title on the y-axis is Distance Traveled in miles. The values on the x-axis are from 0 to 5 in increments of 1 for each grid line. The values on the y-axis are from 0 to 325 in increments of 65 for each grid line. A line is shown connecting ordered pairs 1, 65 and 2, 130 and 3, 195 and 4, 260. The title of the graph is Rate of Travel. What is the rate of change for the relationship represented in the graph? (1 point) fraction 1 over 65 fraction 1 over 64 64 65

Answers

Answer:

The rate of change is 65 miles per hour.

Step-by-step explanation:

The rate of change is the slope, m. To find the slope, use any pair of points.

$m = (y_2 - y_1)/(x_2 - x_1)$

We will use points (1, 65) and (2, 130).

$m = (130 - 65)/(2 - 1)$

$m = (65)/(1)$

The rate of change is 65 miles per hour.

Answer:

I doing this so you can give the other person brainliest....

Step-by-step explanation:

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To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 5 units and 9 units.

Answers

Answer:

The graph of f(x) shifts 5 units right and 9 units down to graph g(x).

Step-by-step explanation:

The general form of the parabola is

$h(x)=a(x-h)^2+k$

Where, (h,k) is the vertex of the parabola and a is stretch factor.

The parent function is

$f(x)=x^2$

The vertex of the parabola is (0,0).

The given function is

$g(x)=(x-5)^2-9$

The vertex of the parabola is (5,-9).

The vertex of the parabola shifts from (0,0) to (5,-9), therefore the graph of f(x) shifts 5 units right and 9 units down to graph g(x).

To graph the function g(x) = (x – 5)2 – 9, shift the graph of f(x) = x2 ✔ right
5 units and ✔ down 9 units.

“In which quadrant would you find point P if the coordinates of P are (–5, ...”Assuming that P is not on an axis, what are the possible answers to this question?
quadrant I or quadrant II
quadrant II or quadrant III
quadrant II or quadrant IV
quadrant III or quadrant IV

Answers

Answer:

quadrant II or quadrant III

Step-by-step explanation:

Quadrants are numbered I to IV in the counterclockwise direction, starting with upper right. Quadrants II and III are to the left of the y-axis, where x-coordinates are negative.

Answer:

B - quadrant ll or quadrant lll

Step-by-step explanation:

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