An SAT prep course claims to improve the test score of students. The table below shows the scores for seven students the first two times they took the verbal SAT. Before taking the SAT for the second time, each student took a course to try to improve his or her verbal SAT scores. Do these results support the claim that the SAT prep course improves the students' verbal SAT scores?

Let d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course)d=(verbal SAT scores prior to taking the prep course)−(verbal SAT scores after taking the prep course). Use a significance level of α=0.1 for the test. Assume that the verbal SAT scores are normally distributed for the population of students both before and after taking the SAT prep course.

Student 1 2 3 4 5 6 7
Score on first SAT 500 380 560 430 450 360 560
Score on second SAT 540 470 580 450 480 400 600

Required:
a. State the null and alternative hypotheses for the test.
b. Find the value of the standard deviation of the paired differences. Round your answer to one decimal place.
c. Compute the value of the test statistic. Round your answer to three decimal places.
d. Determine the decision rule for rejecting the null hypothesis. Round the numerical portion of your answer to three decimal places.
e. Make the decision for the hypothesis test.

Answer:

Since the calculated value of t = -0.215  falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05.

e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.

Step-by-step explanation:

Student                        1      2      3       4      5         6          7

Score on first SAT    500   380 560   430  450    360    560

Score on second SAT 540 470 580  450    480    400    600

Difference d                -40  -90   -20    -20    -30     -40     -40     ∑ -280

d²                               1600  8100 400 400   900   1600  1600   ∑14600

a. Let the hypotheses be

H0:  ud= 0      against the claim Ha: ud ≠0

The degrees of freedom = n-1= 7-1= 6

The significance level is 0.05

The test statistic is

t= d`/sd/√n

The critical region is ║t║≤ t (0.025,6) = ±2.447

d`= ∑di/n= -280/7= -4

Sd²= ∑(di-d`)²/n-1 = 1/n-1 [∑di²- (∑di)²n]

= 1/6[14600-(-4)²/7] = [14600-2.2857/6]= 2432.952

b. Sd= 49.3249= 49.325

Therefore

c. t= d`/ sd/√n

t=   -4/ 49.325/√7

t= -4/18.6435 = -0.2145= -0.215

d. Since the calculated value of t = -0.215  falls in the critical region so we accept Ha that SAT prep course improves the students' verbal SAT scores and reject the null hypothesis at significance level 0.05

e. These results support the claim that the SAT prep course improves the students' verbal SAT scores.

hiking boots cost $99.55 they are on sale for $15.18 off. what is the percent of discount

5 What is -5 –+3 2 2.
​

Use slopes to determine whether the lines AB and CD are parallel, perpendicular, or neither. SHOW WORK
A(-10, 8) and B (-9,4).
C (-5, 12) and D (2,9).

Solve for x.
14 + 3x = 2 + 9x
You don’t have to do an explanation

suris age is 4 less than 3 times her cousins age. suri is 17 years old. which method can be used to find c, her cousins age?

5. 3y(4 + 5x) *
(1 Point)
12y + 15x
12y + 15xy
4 + 15x

5 star rating help quick

What are some things to be aware of that can lead to higher than expected totals when making a purchase or checking out

Laura earned $250 on her money market investment over a 2
year period of time. The interest rate during this period of time
was 5% annually. How much money did Laura invest in the
money market from the start?
A) $250
B) $500
C) $2000
D) $2500

1010 rubber stamps cost \$10.30$10.30dollar sign, 10, point, 30.
Which equation would help determine the cost of 222 rubber stamps?
Choose 1 answer:
Choose 1 answer:

(Choice A)
A
\dfrac{2}{x} = \dfrac{\$10.30}{10}
x
2
​
=
10
$10.30
​
start fraction, 2, divided by, x, end fraction, equals, start fraction, dollar sign, 10, point, 30, divided by, 10, end fraction

(Choice B)
B
\dfrac{x}{2} = \dfrac{10}{\$10.30}
2
x
​
=
$10.30
10
​
start fraction, x, divided by, 2, end fraction, equals, start fraction, 10, divided by, dollar sign, 10, point, 30, end fraction

(Choice C)
C
\dfrac{2}{10} = \dfrac{\$10.30}{x}
10
2
​
=
x
$10.30
​
start fraction, 2, divided by, 10, end fraction, equals, start fraction, dollar sign, 10, point, 30, divided by, x, end fraction

(Choice D)
D
\dfrac{2}{\$10.30} = \dfrac{x}{10}
$10.30
2
​
=
10
x
​
start fraction, 2, divided by, dollar sign, 10, point, 30, end fraction, equals, start fraction, x, divided by, 10, end fraction

(Choice E, Checked)
E
None of the above

Solve nine eighteenths plus one third

Daniel buys two apples for every five oranges. If you bought 12 apples, how many oranges dis he buy?

What is the product?
3.[ 1 -4 5 -7]

a. [3 -12 15 -21]
b. [4 -1 8 -4]
c. [3 12 15 21]
d. [4 -12 8 -21]

Simplify:(-3x3)(-2x)
A. -5x15
B
6x15
–5x²
6x

Please help me I’m begging u it’s due in 10 minutes!!

will give brainlest

What property is demonstrated by the way in which numbers are grouped when they are added or multiplied and it does not change their sum or product?
Group of answer choices

Identity Property

Distributive Property

Associative Property

Commutative Property

HELP PLEASE 18 POINTS

help! i will mark brainliest!

Diego had $420 in his checking account. He made 6 deposits of $35.50 each. He also
needs to write 4 checks for $310.75 each.
a. How much did Diego deposit In total?

show the work please.
giving 13 points!!

Victor purchased motor oil for $2 a bottle and car wax for $4 a bottle. The inequality 2x + 4y < 16 can
be used to determine the number of bottles of motor oil, x, and the number of bottles of car wax, y,
Victor purchased for less than $16, not including tax. Which of the following ordered pairs best
represents a reasonable combination of bottles of motor oil and car wax that Victor could have
purchased?

6x + 15xy
Looking For Factor

graph each function (equation) by making a table y = |2x| + 1

please help​

If d= 2, what is the value of 8/(4-d)? A.1
B. 4/3
C. 4
D. 0​

PLEASE ANSWER ASASSP!!!!!!!!!!!!!!!!!!!!
Sovle the equation
6 (y + 1.5) = -18
What is y?

Floyd is an aspiring music artist. He has a record contract that pays him a base rate of \$200$200dollar sign, 200 a month and an additional \$12$12dollar sign, 12 for each album that he sells. Last month he earned a total of \$644$644dollar sign, 644.
Write an equation to determine the number of albums (a)(a)left parenthesis, a, right parenthesis Floyd sold last month.

Item 6
At the beginning of the day, the temperature is -8°F. As the sun comes out, it warms up 19°F. What is the temperature once it warms up?
°F

The lgrsedfaffedadwaawdwaffweaf

1.)
a^2b^3
---------- <-----write in expanded form.
cd


2.)what is the exact solution to the equation 4^5x=3^x-2

Please show all work I've been struggling to understand these questions!!!! thank you so much <3

Which expression represents "8 times the difference of 52 and 9"?

Pls helpp ill mark brainlist