1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Elan Coil [88]
3 years ago
6

Two researchers conducted a study in which two groups of students were asked to answer 42 trivia questions from a board game. Th

e students in group 1 were asked to spend 5 minutes thinking about what it would mean to be a​ professor, while the students in group 2 were asked to think about soccer hooligans. These pretest thoughts are a form of priming. The 200 students in group 1 had a mean score of 21.9 with a standard deviation of 3.4​, while the 200 students in group 2 had a mean score of 19.8 with a standard deviation of 3.5.
(a) Determine the 95% confidence interval for the difference in scores μ1 - μ2.
Mathematics
1 answer:
Verizon [17]3 years ago
5 0

Answer:

(21.9-19.8) -1.966\sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 1.422

(21.9-19.8) -1.966 \sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 2.778

And we are 95% confident that the true difference means are between 1.422 \leq \mu_1 -\mu_2 \leq 2.778

Step-by-step explanation:

We know the following info:

\bar X_1 = 21.9 sample mean for group 1

\bar X_2 = 19.8 sample mean for group 2

s_1 = 3.4 sample standard deviation for group 1

s_2 = 3.5 sample standard deviation for group 2

n_1 = 200 sample size group 1

n_2 = 200 sample size group 2

We want to find a confidence interval for the difference of means and the correct formula to do this is:

(\bar X_1 -\bar X_2) \pm t_{\alpha/2} \sqrt{\frac{s^2_1}{n_1} +\frac{s^2_2}{n_2}}

Now we just need to find the critical value. The confidence level is 0.95 then the significance is 1-0.95 =0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df= n_1 +n_2 -2= 200+200-2= 398

The critical value for this case would be :t_{\alpha/2}=1.966  

And replacing into the confidence interval formula we got:

(21.9-19.8) -1.966\sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 1.422

(21.9-19.8) -1.966 \sqrt{\frac{3.4^2}{200} +\frac{3.5^2}{200}}= 2.778

And we are 95% confident that the true difference means are between 1.422 \leq \mu_1 -\mu_2 \leq 2.778

You might be interested in
Om to 4conm.
max2010maxim [7]
The correct answer is water
8 0
3 years ago
The polynomial of degree 4, P ( x ) , has a root of multiplicity 2 at x = 1 and roots of multiplicity 1 at x = 0 and x = − 2 . I
ICE Princess25 [194]

We want to find a polynomial given that we know its roots and a point on the graph.

We will find the polynomial:

p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x

We know that for a polynomial with roots {x₁, x₂, ..., xₙ} and a leading coefficient a, we can write the polynomial equation as:

p(x) = a*(x - x₁)*(x - x₂)...*(x - xₙ)

Here we know that the roots are:

  • x = 1 (two times)
  • x = 0
  • x = -2

Then the roots are: {1, 1, 0, -2}

We can write the polynomial as:

p(x) = a*(x - 1)*(x - 1)(x - 0)*(x - (-2))

p(x) = a*(x - 1)*(x - 1)*(x + 2)*x

We also know that this polynomial goes through the point (5, 336).

This means that:

p(5) = 336

Then we can solve:

336 = a*(5 - 1)*(5 - 1)*(5 + 2)*5

336 = a*(4)*(4)*(7)*5

336 = a*560

366/560 = a = 183/280

Then the polynomial is:

p(x) = (183/280)*(x - 1)*(x - 1)*(x + 2)*x

If you want to learn more, you can read:

brainly.com/question/11536910

5 0
2 years ago
There are 24 children on playground. 3/4 are playing soccer. How many children are not playing soccer?
Zinaida [17]

Answer:

18

Step-by-step explanation:

To find the answer, multiply 24 by 3/4 or 0.75 to make it easier. 24 multiplied by 0.75 in a calculator is 18.

3 0
2 years ago
Read 2 more answers
Name four angles between 0 and 360 degrees with a reference angle of 20 degrees Show work
Archy [21]
20, 180 - 20, 180 + 20 and 360 - 20

i.e. 20°, 160°, 200° and 340°
5 0
3 years ago
Read 2 more answers
A line that intersects two or more lines is called a parallel line true or false
Irina18 [472]

Answer:

False

Step-by-step explanation:

Parallel lines never touch

6 0
3 years ago
Other questions:
  • Plzzzzz help I’ll mark brainlest thxxxx
    7·1 answer
  • A regression model in which more than one independent variable is used to predict the dependent variable is called
    6·1 answer
  • What is 60 percent written as decimal
    7·1 answer
  • Mr. Evans displays the test scores of his first period class in the box plot below.
    13·2 answers
  • Writed each decimal that is -0.85
    7·1 answer
  • If the density of iron is 7.8 g/cm3 and you find an iron nail weighing 15g, what would the volume of the nail be?
    5·2 answers
  • Find an equation of the line parallel to y=2x+3 and that passes through the point (5,3)
    8·2 answers
  • A newspaper advertisement offers a $6500 used car for nothing down and 36 easy monthly payments of
    6·1 answer
  • Number 13. Multiply please.
    9·1 answer
  • 1. Given a right circular conea) What is the shape of a cross section parallel to the base of the cone?b) what is the shape of a
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!