A certain test preparation course is designed to help students improve their scores on the USMLE 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 3 students' scores on the exam after completing the course:
15,20,18
Using these data, construct a 90% confidence interval for the average net change in a student's score after completing the course. Assume the population is approximately normal.

Answer:

The 90% confidence interval for the average net change in a student's score after completing the course is (13.42, 21.92).

Step-by-step explanation:

Average change in the sample:

[tex]M_{s} = \frac{15+20+18}{3} = 17.67[/tex]

Standard deviation of the sample:

[tex]s = \sqrt{\frac{(15-17.67)^2+(20-17.67)^2+(18-17.67)^2}{2}} = 2.52[/tex]

We have the standard deviation for the sample, so the t distribution is used.

The first step to solve this problem is finding how many degrees of freedom, we have. This is the sample size subtracted by 1. So

df = 3 - 1 = 2

90% confidence interval

Now, we have to find a value of T, which is found looking at the t table, with 2 degrees of freedom(y-axis) and a confidence level of [tex]1 - \frac{1 - 0.9}{2} = 0.95[/tex]. So we have T = 2.92

The margin of error is:

[tex]M = T\frac{s}{\sqrt{n}} = 2.92\frac{2.52}{\sqrt{3}} = 4.25[/tex]

In which s is the standard deviation of the sample and n is the size of the sample.

The lower end of the interval is the sample mean subtracted by M. So it is 17.67 - 4.25 = 13.42

The upper end of the interval is the sample mean added to M. So it is 17.67 + 4.25 = 21.92

The 90% confidence interval for the average net change in a student's score after completing the course is (13.42, 21.92).

Dan bought 5 new baseball trading cards to add to his collection. The next day his dog ate half of his collection. There are now only 46 cards left. How many cards did Dan start with ? show equation

Unit 11: Volume & Surface Area
Homework 1: Area of Plane Figures
Directions: Find the area of each figure. Round to the nearest hundredth where necessary.
2. and 11. all I need
will give brainliest if u get it right I promise​

Each letter of the word "rainbow" has been written on a separate slip of paper and put into a box. Find the probability of selecting a slip of paper with a vowel on it, replacing it, then selecting the letter w?

Which would be the best trend line for the given data set?
A) y=x+4
B) y=-x+4
C) y=-1/4x+2
D) 1/4x+2

4, 2, 1, 2, ...
O Arithmetic
O Geometric
O Neither

helppppppppppppppppppppppppp

What is the slope of the line?

Micah and his brother found some cash at
a bus stop. They split the money evenly, each
getting $ 16. How much money did they find?
m

5+6(2x-1)
i need this like now pls

Need the answer fast question is on the problem will mark brainliest
NO LINKS PLEASE

Find the surface area of the cylinder. ROUND YOUR ANSWER TO THE NEAREST TENTH. PLEASE I NEED HELP also if anyone can I need the steps:(

f(x)=3(x-2)^2 +5 Find Vertex of Parabola given.

Simplify the following polynomial expression.
(534 – 933 + 73 – 1) + (-804 + 4.12 – 3x + 2) - (-413 + 51 – 1)(21 – 7)
OA. 504 – 3723 - 612 + 411 - 8
OB. 524 – 3723 - 6x2 + 411 - 6
OC. 11,4 – 21.13 + 14x2 + 331 - 6
OD. 11,4 – 2113 + 14.2 + 33.3 - 8

A right triangle has legs that are 21 in. and 25 in. long. What is the area of the triangle?

Janice Davidson, single mother of two in her late 20s, manages an in-store boutique at Lacy's Department Store. She earns $60,000 a year before taxes (her gross income) and pays 20% in taxes. Janice's fixed monthly living expenses are $2,400 with another $1,600 in variable/discretionary living expenses. Janice has $13,000 in emergency savings. Janice has an employer-paid disability benefit through the department store where she works. Lacy's provides its employees a long-term disability insurance benefit that pays 60% of an employee's gross salary up to a maximum of $5,000 a month. Would a policy that pays 40% of her gross salary provide enough income to cover Janice's fixed monthly expenses if she became disabled and couldn't work? If yes, how much could she set aside each month after fixed expenses are paid? If no, how much of a shortfall would she have and how could she cover it?​

Please Help due in 1 min

No Links Allowed

please answer this thanks

Determine the coordinates of the y-intercept of the function shown in the graph.
A)
(0, -1)
B)
(2,0)
9
(0,2)
D)
(-1,0)
Includes the photo for the question

A lawn is shaped like a parallelogram with a base of 30 feet and a height of 12 feet. Covering the lawn with grass will cost $2.60 per square foot. How much money will it cost to cover the lawn with grass?

what is the definition of corresponding sides​

Need help please I will mark brainlist

helppppppp will give BRAINLIEST!!!

NO LINKS!!! Plz help this is due tmr

There are 15 boys in the class of 40 learners. What is the ratio of boys to girls in the classroom????​

Can you help I’m in middle school and cant get this!

A veterinarian in Camperville zoo needs to weigh the big bear. Which would be the most appropriate unit of measure?
A. meters
B. kilograms
C. liters
D. cups

Pamela is 9 years younger than Jiri. The sum of their ages is 53. What is Jiri's age?

Can someone please answer this

Pls help put in order 1,2,3,4,5,6,7,8,9,10 I will give brainlyest

I need help please
Please hurry