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
IgorC [24]
3 years ago
7

A practice law exam has 100 questions, each with 5 possible choices. A student took the exam and received 13 out of 100.If the s

tudent guesses the whole test, the expected number of correct answers is 20 with a standard error of .Compute the z-test statistic for the observed value 13.Find the observed significance level or P-value of the statistic.
Mathematics
1 answer:
Cloud [144]3 years ago
5 0

Answer:

z=\frac{13-20}{4}=-1.75

Assuming:

H0: \mu \geq 20

H1: \mu

p_v = P(Z

Step-by-step explanation:

The binomial distribution is a "DISCRETE probability distribution that summarizes the probability that a value will take one of two independent values under a given set of parameters. The assumptions for the binomial distribution are that there is only one outcome for each trial, each trial has the same probability of success, and each trial is mutually exclusive, or independent of each other".

Let X the random variable of interest (number of correct answers in the test), on this case we now that:

X \sim Binom(n=100, p=0.2)

The probability mass function for the Binomial distribution is given as:

P(X)=(nCx)(p)^x (1-p)^{n-x}

Where (nCx) means combinatory and it's given by this formula:

nCx=\frac{n!}{(n-x)! x!}

We need to check the conditions in order to use the normal approximation.

np=100*0.2=20 \geq 10

n(1-p)=20*(1-0.2)=16 \geq 10

So we see that we satisfy the conditions and then we can apply the approximation.

If we appply the approximation the new mean and standard deviation are:

E(X)=np=100*0.2=20

\sigma=\sqrt{np(1-p)}=\sqrt{100*0.2(1-0.2)}=4

So we can approximate the random variable X like this:

X\sim N(\mu =20, \sigma=4)

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".

The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".  The letter \phi(b) is used to denote the cumulative area for a b quantile on the normal standard distribution, or in other words: \phi(b)=P(z

The z score is given by this formula:

z=\frac{x-\mu}{\sigma}

If we replace we got:

z=\frac{13-20}{4}=-1.75

Let's assume that we conduct the following test:

H0: \mu \geq 20

H1: \mu

We want to check is the score for the student is significantly less than the expected value using random guessing.

So on this case since we have the statistic we can calculate the p value on this way:

p_v = P(Z

You might be interested in
In the circle shown, BD is a diameter, m1 = 100° and m = 30°. m3 = _____
morpeh [17]
If a cirlce is 360* the cloest answer would have to be.... *c*
3 0
3 years ago
Find the measure of x and round to the nearest tenth!!
Jet001 [13]

Answer:24

Step-by-step explanation:

the number of the right triangle is to subtract the number

4 0
3 years ago
Round 5,439 to the nearest thousand​
Murrr4er [49]

Answer:

5,000

Step-by-step explanation:

4 is less than 5 and more so, it will leave the 5 alone

It will also turn everything else into 0's. Making it:

-------------------------------------------------------------------------------

5,000

7 0
3 years ago
Help!!!! I need it ASAP!! I am confused. Am I on the right track
melisa1 [442]

Answer:

x = 7

y = 0

Step-by-step explanation:

Close, but not quite.

8 0
3 years ago
The two triangles are similar. Which statements are true? Select each correct statement. ∠A≅∠D BDBA=DEAC BDBA=DEBC ∠B≅∠E Triangl
horsena [70]

Answer:

SR/BC=RT/CA    And  /R=/C  S B And D

Step-by-step explanation:

Just Look at them then compare its pretty simple you just have to think about it.

5 0
3 years ago
Other questions:
  • Marianne has 5/8 pound of peas she cooks 2/3 of those peas for five people if each person is served an equal amount how much pea
    14·1 answer
  • a rectangle has a length of 3/81 and a width of 3^2/3 inches. find the area of the rectangle. a. 3^2/3 inches squared b. 3^8/3 i
    9·1 answer
  • 9 x n -20 = 16 what is n?
    10·1 answer
  • Cassie has 8 red marbles and 12 yellow marbles. Her mom doubles her red and yellow marbles. Use the distributive property to sho
    13·2 answers
  • Hillel is juggling flaming torches to raise money for charity. His initial appearance raises $500, and he raises $15 for each mi
    15·2 answers
  • If 6% of the 205 million adult Americans are unemployed, how many adult Americans are unemployed?
    5·2 answers
  • Use the data in the table to find the median mode, and range of the data.
    11·2 answers
  • Help me plz, 13 points! these questions are separate. help me work out both questions please ​
    6·1 answer
  • Two thirds a number x plus 3 is 6
    10·1 answer
  • Find the perimeter of the polygon with the given vertices. C(4, -1), D(4,−5), E(2,−3)
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!