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
Mnenie [13.5K]
3 years ago
10

A random sample of 16 students selected from the student body of a large university had an average age of 25 years and a populat

ion standard deviation of 2 years. We want to determine if the average age of all the students at the university is significantly more than 24. Assume the distribution of the population of ages is normal.
What is the alternative and null hypotheses?
What is the test statistic?
What is the p-value?
What is your conclusion about the stated hypotheses at a 95% confidence level?
Mathematics
1 answer:
eimsori [14]3 years ago
3 0

Answer:

t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2      

p_v =P(t_{15}>2)=0.0320  

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.  

Step-by-step explanation:

1) Data given and notation      

\bar X=25 represent the sample mean      

s=2 represent the standard deviation for the sample      

n=16 sample size      

\mu_o =24 represent the value that we want to test    

\alpha represent the significance level for the hypothesis test.    

t would represent the statistic (variable of interest)      

p_v represent the p value for the test (variable of interest)  

Confidence =0.95 or 95%

\alpha=0.05

State the null and alternative hypotheses.      

We need to conduct a hypothesis in order to determine if the mean is higher than 24, the system of hypothesis would be:      

Null hypothesis:\mu \leq 24      

Alternative hypothesis:\mu > 24      

We don't know the population deviation, so for this case is better apply a t test to compare the actual mean to the reference value, and the statistic is given by:      

t=\frac{\bar X-\mu_o}{\frac{s}{\sqrt{n}}} (1)      

t-test: "Is used to compare group means. Is one of the most common tests and is used to determine if the mean is (higher, less or not equal) to an specified value".  

Calculate the statistic      

We can replace in formula (1) the info given like this:      

t=\frac{25-24}{\frac{2}{\sqrt{16}}}=2      

Calculate the P-value      

First we need to calculate the degrees of freedom given by:  

df=n-1=16-1=15  

Since is a one-side upper test the p value would be:      

p_v =P(t_{15}>2)=0.0320  

Conclusion      

If we compare the p value and the significance level given for example \alpha=0.05 we see that p_v so we can conclude that we reject the null hypothesis, and the true mean is significant higher than 24 years.      

You might be interested in
Hi! I need the answer to this quickly! Thank you
geniusboy [140]
I am pretty sure it’s 14 I think but i don’t know for sure
6 0
2 years ago
Read 2 more answers
Janet can get 36-pack of bottled water for $9.60. How much would Janet have to pay for a 12-pack of bottled water if the ratios
Olenka [21]
Janet would have to pay $3.20.
3 0
2 years ago
A fair die with sides numbered 1, 2, 3, 4, 5, and 6 is to be rolled until a number greater than 4 first appears. what is the pro
AnnyKZ [126]
First two rolls have to be 1-4 that is 2/3 chance twice and the third can be 4or 5
2/3*2/3*1/3 + the chance that the fourth is the 5 or 6. 
2/3*2/3*2/3*1/3

So the solution is : P=2/3*2/3*1/3 + 2/3*2/3*2/3*1/3
7 0
3 years ago
What is the solution of the following system
AleksAgata [21]

Step-by-step explanation:

8x + 14y = 4 ...1

-6x - 7y = -10 ...2

...2 × 2 in 2 sides of the equation

-12x -14y = -20 ...3

...1 + ...3

8x + 14y +(-12x -14y) = 4 +(-20)

8x + 14y - 12x -14y = 4 - 20

-4x = -16

x = (-16)/(-4)

= 4

replace x in ...1 or ...2 you will reserve y value

and answer in the term of (x,y)

4 0
3 years ago
Help please give answer please
Vsevolod [243]

The mean is 8 gerbils and the MAD is 4.29.

<h3>What is the mean?</h3>

Mean is the average of a set of numbers. It is determined by adding the numbers together and dividing it by the total number

Mean = sum of the numbers / total number

(0 + 3 + 6 + 9 + 11 + 13 + 14) / 7 = 8

What is the MAD?

MAD =  ∑ l x - m(x) l

| (0 - 8) + (3 - 8) + (6 - 8) + (9 - 8) + (11 - 8) + (13 - 8) + (14 - 8)| / 7 = 4.29

To learn more about mean, please check: brainly.com/question/25842202

#SPJ1

3 0
1 year ago
Other questions:
  • One fifth of the difference of a number and 1 in an expression
    14·1 answer
  • Clara is growing her hair out and wants it to be no longer than 15 cm but more than 11 cm. Her hair is 7 cm right now and grows
    12·1 answer
  • What is the values of x and y? <br><br> (5x) + (9y)
    7·1 answer
  • Put these fraction in order of size smallest to largest : 7/10, 2/3, 4/5, 11/15
    5·2 answers
  • The depth of a pool is 9.2789.278 feet. Round the depth to the nearest tenth of a foot.
    15·2 answers
  • Please help!! Which two equations are the equations of vertical asymptotes of the function y = 5∕3 tan(3∕4x)?
    7·2 answers
  • Tristen is packing lunch boxes for the school trip. Each lunch box consists of 1 sandwich, 1 fruit, and 1 drink. Tristen can cho
    10·1 answer
  • Suppose 53% of the students in a university are baseball players. If a sample of 400 students is selected, what is the probabili
    7·1 answer
  • en una granja sembraron 20 parcelas de locotes, con 40 plantas en cada una ¿Cuántas plantas de locotes se tienes?
    7·1 answer
  • Square root of 342354456​
    13·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!