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
Anastaziya [24]
2 years ago
12

A college counselor is interested in estimating how many credits a student typically enrolls in each semester. The counselor dec

ides to randomly sample 100 students by using the registrar's database of students. The histogram below shows the distribution of the number of credits taken by these students. Sample statistics for this distribution are also provided.Min Q1 Median Mean SD Q3 Max
8 13 14 13.65 1.91 15 18

(a) Based on this data, would you accept or reject the hypothesis that the usual load is 13 credits?

(b) How unlikely is it that a student at this college takes 16 or more credits?
Mathematics
2 answers:
pshichka [43]2 years ago
6 0

Answer:

(a) We reject the null hypothesis that usual load is 13 credits.

(b) Probability that student at this college takes 16 or more credits = 0.10935

Step-by-step explanation:

We are given that the histogram below shows the distribution of the number of credits taken by these students;

 Min   Q1    Median     Mean      SD     Q3      Max

   8     13         14           13.65     1.91      15        18

Also, the counselor decides to randomly sample 100 students by using the registrar's database of students, i.e., n = 100.

So, Null Hypothesis, H_0 : \mu = 13 {means that the usual load is 13 credits}

Alternate Hypothesis, H_1 : \mu\neq 13 {means that the usual load is not 13 credits}

The test statistics we will use here is ;

              T.S. = \frac{Xbar - \mu}{\frac{s}{\sqrt{n} } } ~ t_n_-_1

where, Xbar = sample mean = 13.65

               s = sample standard deviation = 1.91

               n = sample size = 100

So, test statistics = \frac{13.65 - 13}{\frac{1.91}{\sqrt{100} } } ~ t_9_9

                            = 3.403

Now, since significance level is not given to us so we assume it to be 5%.

At 5% significance level, the t tables gives critical value of 1.987 at 99 degree of freedom. Since our test statistics is more than the critical value which means our test statistics will lie in the rejection region, so we have sufficient evidence to reject null hypothesis.

Therefore, we conclude that the usual load is not 13 credits.

(b) Let X = credits of students

The z score probability distribution is given by;

         Z = \frac{X-\mu}{\sigma} ~ N(0,1)

So, probability that student at this college takes 16 or more credits =     P(X \geq 16)

P(X \geq 16) = P( \frac{X-\mu}{\sigma} \geq \frac{16-13.65}{1.91} ) = P(Z \geq 1.23) = 1 - P(Z < 1.23)

                                                 = 1 - 0.89065 = 0.10935 or 11%

Therefore, probability that student at this college takes 16 or more credits is 0.10935.

Ket [755]2 years ago
3 0

Answer:

(a) The usual load is not 13 credits.

(b) The probability that a a student at this college takes 16 or more credits is 0.1093.

Step-by-step explanation:

According to the Central limit theorem, if a large sample (<em>n</em> ≥ 30) is selected from an unknown population then the sampling distribution of sample mean follows a Normal distribution.

The information provided is:

Min.=8\\Q_{1}=13\\Median=14\\Mean=13.65\\SD=1.91\\Q_{3}=15\\Max.=18

The sample size is, <em>n</em> = 100.

The sample size is large enough for estimating the population mean from the sample mean and the population standard deviation from the sample standard deviation.

So,

\mu_{\bar x}=\bar x=13.65\\SE=\frac{s}{\sqrt{n}}=\frac{1.91}{\sqrt{100}}=0.191

(a)

The null hypothesis is:

<em>H</em>₀: The usual load is 13 credits, i.e. <em>μ</em> = 13.

Assume that the significance level of the test is, <em>α</em> = 0.05.

Construct a (1 - <em>α</em>) % confidence interval for population mean to check the claim.

The (1 - <em>α</em>) % confidence interval for population mean is given by:

CI=\bar x\pm z_{\alpha/2}\times SE

For 5% level of significance the two tailed critical value of <em>z</em> is:

z_{\alpha/2}=z_{0.05/2}=z_{0.025}=1.96

Construct the 95% confidence interval as follows:

CI=\bar x\pm z_{\alpha/2}\times SE\\=13.65\pm (1.96\times0.191)\\=13.65\pm0.3744\\=(13.2756, 14.0244)\\=(13.28, 14.02)

As the null value, <em>μ</em> = 13 is not included in the 95% confidence interval the null hypothesis will be rejected.

Thus, it can be concluded that the usual load is not 13 credits.

(b)

Compute the probability that a a student at this college takes 16 or more credits as follows:

P(X\geq 16)=P(\frac{X-\mu}{\sigma}\geq \frac{16-13.65}{1.91})\\=P(Z>1.23)\\=1-P(Z

Thus, the probability that a a student at this college takes 16 or more credits is 0.1093.

You might be interested in
Question 6. Which expression is equivalent to this expression? x(2x + 3)
suter [353]

Answer:

The answer is D

You have to distribute the x to the 2x + 3 equation

This will result in 2x^2 + 3x

5 0
2 years ago
Read 2 more answers
How is this problem factored? 35x^2-57x-44
faust18 [17]
You can use the quadratic formula with it which will be easier 
or simple factoring 
it will be (5x-11)(7x+4)
7 0
2 years ago
A rectangular solid has width w, a length of 7 more than the width, and a height that is equivalent to 15 decreased by 3 times t
Helen [10]

Answer:

njgrjn djgb E THE ANSWER IS 3

Step-by-step explanation:

jbuyf6ctvyhbjnkmljinhubygvtb njmkbbhjcghxfgvjctguhvjhbjbhbyguyc

7 0
2 years ago
Angie baked 100 cookies, and 20 brownies. She wants to split them into equal groups for the bake sale .Each group must have the
densk [106]
20 is the greatest common factor Each group of 20 will have 1 brownie & 5 cookies
6 0
3 years ago
Find the solution of this system of equations. separate the x and y values.<br> x=2+y<br> -6x-6y=-12
Shkiper50 [21]
{x=2+y
{-6x-6y=-12

-6(2+y) -6y = -12
-12 - 6y - 6y = -12
-12y = -12 + 12
-12y = 0
y = 0

x = 2 + y = 2 + 0 = 2

Answer: x=2, y=0
8 0
3 years ago
Other questions:
  • Enter a range of values for x.<br> 85°<br> 25<br> 5x - 10<br> [ ? ] Enter
    15·1 answer
  • -2n(5+n-8-3n) n =3 algebra
    14·1 answer
  • What is the completely factored form of f(x) = x^3 – 2x^2 – 5x + 6?
    8·1 answer
  • I need help with this homework question
    7·2 answers
  • Which set of measurements forms a right triangle? Use the Pythagorean theorem: a2 + b2 = c2.
    10·1 answer
  • Michael wanted to make another quilt with an area of 42 square feet. What are its possible dimensions of they must be whole numb
    14·1 answer
  • Pls help me out<br> image is down below
    7·1 answer
  • (02.05 MC)<br> Determine if the two figures are congruent and explain your answer. (10 points)
    9·1 answer
  • Distributive property.<br><br> 1. -5(y + 1) + 6y<br> 2. 4(z-2)+3z<br> 3. (f-5)(-2)+ 11f
    6·1 answer
  • Decide if the following statement is valid or invalid. If two sides of a triangle are congruent then the triangle is isosceles.
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!