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
Ipatiy [6.2K]
3 years ago
8

A random sample of 225 measurements is selected from a population, and the sample mean and standard deviation are x =32.5 and s

= 30.0, respectively. It is claimed that the population mean exceeds 30. State the null and an appropriate alternative hypothesis, and perform a test at 5% significance level.
Mathematics
1 answer:
AlexFokin [52]3 years ago
4 0

Answer:

t=\frac{32.5-30}{\frac{30}{\sqrt{225}}}=1.25    

p_v =P(t_{(224)}>1.25)=0.106  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.

Step-by-step explanation:

Data given and notation  

\bar X=32.5 represent the sample mean  

s=30 represent the sample standard deviation

n=225 sample size  

\mu_o =30 represent the value that we want to test

\alpha=0.05 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)  

State the null and alternative hypotheses.  

We need to conduct a hypothesis in order to check if the mean exceeds 30, the system of hypothesis would be:  

Null hypothesis:\mu \leq 30  

Alternative hypothesis:\mu > 30  

If we analyze the size for the sample is > 30 but we don't know the population deviation so 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{32.5-30}{\frac{30}{\sqrt{225}}}=1.25    

P-value

The first step is calculate the degrees of freedom, on this case:  

df=n-1=225-1=224  

Since is a one side rigth tailed test the p value would be:  

p_v =P(t_{(224)}>1.25)=0.106  

Conclusion  

If we compare the p value and the significance level given \alpha=0.05 we see that p_v>\alpha so we can conclude that we have enough evidence to FAIL to reject the null hypothesis, so we can't conclude that the true mean is actually its significantly higher than 30.  

You might be interested in
A surveyor is standing 118 feet from the base of the Washington Monument. The surveyor measures the angles between the ground an
jeka57 [31]
The height of the Washington monument is 555.146.

I got this by using trigonometry “tan(77) • 118”
7 0
3 years ago
Bobby earns $120 by shoveling 6 driveways. How much will he earn if he shovels 10 driveway
pogonyaev
120/6=20 20*10=200 
The answer is 200
5 0
3 years ago
Read 2 more answers
1) what is 1/5 times 1/2 ?
Savatey [412]
1. 1/10
2. 3/5
3. 1/10
4. 1/6
5. 3/14
8 0
3 years ago
Create at least two word problems that involve addition, subtraction, multiplication and division.
never [62]
John brought 20 water melons each water melon cost him 2 dollars. He gave his friend Bob 3/4 of the watermelons. In return bob gave him double the amount of water melons back. How many watermelons does John have now? How much money did he spend on each water melon?
8 0
2 years ago
Write a polynomial equation with integer coefficients that has the given roots x=1, x=-4
Gekata [30.6K]
(x -1)(x +4) = 0

x² +3x -4 = 0 . . . . . . probably the form you're looking for
7 0
3 years ago
Read 2 more answers
Other questions:
  • Finding the Slope of a Line on a Graph
    10·1 answer
  • Assign every student at Coggins Middle School a number then use a random number generator to select the numbers.
    13·1 answer
  • Round each time to the nearest whole second. Then estimate how many seconds bailey won the race by.
    5·2 answers
  • What is the eighth term in the arithmetic sequence 1,10,19,28
    12·1 answer
  • (x/2 + bb) 10 x=7 b=2
    9·1 answer
  • Which measurement is most accurate to describe the weight of an apple?
    10·1 answer
  • Please help asap.....​
    8·1 answer
  • Got a question on my math quiz asking the question below. It marked me as wrong but it didn’t tell me what I got right/wrong. Co
    7·1 answer
  • Someone please help:)
    11·1 answer
  • Plsss help me with thiss !!!
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!