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
VARVARA [1.3K]
3 years ago
14

The mean consumption of water per household in a city was 1425 cubic feet per month. Due to a water shortage because of a drough

t, the city council campaigned for water use conservation by households. A few months after the campaign was started, the mean consumption of water for a sample of 100 households was found to be 1175 cubic feet per month. The population standard deviation is given to be 250 cubic feet.
A. Find the p-value for the hypothesis test that the mean consumption of water per household has decreased due to the campaign by the city council. Would you reject the null hypothesis at α = .025?

B. Make the test of part A using the critical-value approach and α = .025
Mathematics
1 answer:
liberstina [14]3 years ago
6 0

Answer:

a)t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10    

The degrees of freedom are given by:

df=n-1=100-1=99  

The p value for this case would be given by:

p_v =P(t_{99}  

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

b) For this case we need to find a critical value in the t distribution with  99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

t_{\alpha/2}=1.984

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

Step-by-step explanation:

Information given

\bar X=1175 represent the sample mean for the cubic feets of households

\sigma=250 represent the population standard deviation

n=100 sample size  

\mu_o =1425 represent the value to verify

\alpha=0.025 represent the significance level

t would represent the statistic

p_v represent the p value

Part a

We want to test that the mean consumption of water per household has decreased due to the campaign by the city council, the system of hypothesis would be:  

Null hypothesis:\mu \geq 1425  

Alternative hypothesis:\mu < 1425  

Since we don't know the deviation the statistic is given by:

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

The statistic is given by:

t=\frac{1175-1425}{\frac{250}{\sqrt{100}}}=-10    

The degrees of freedom are given by:

df=n-1=100-1=99  

The p value for this case would be given by:

p_v =P(t_{99}  

Since the p value is significantly lower than he significance level given we have enough evidence to reject the null hypothesis and we can conclude that the true mean is lower than 1425

Part b

For this case we need to find a critical value in the t distribution with  99 degrees of freedom who accumulates 0.025 of the area in the right tail and we got:

t_{\alpha/2}=1.984

Since the calculated value is higher than the critical value we can reject the null hypothesis at the significance level provided and we can say that the true mean is higher than 1425

You might be interested in
WORTH 10 POINTS! 1)susan can type 4 pages of text in 10 minutes.Assuming she types at a constant rate,write the linear equation
Minchanka [31]
1) pages per minute is the rate. the rate is the slope pages/minutes = .4
y=.4x or y=2/5(x)
2)birdhouses per day is the slope. = .6
y=.6x or y=3/5(x)
3) miles per hour is the slope. 500/8=62.5
y=62.5x
4) square feet per minute is the slope. 40/9 =4.444444444
y=4.4444444444x or y=40/9(x)
5)miles per minutes is the rate. 5/41 is the slope. 
y=5/41(x)
6) the rate is square feet per minute. 450/30=15
y=15x
8 0
3 years ago
In which quadrant does the point P(–1, 5) lie? III II IV I
snow_tiger [21]
4 ........................................
7 0
3 years ago
Read 2 more answers
Which circle will have the largest circumference?
Dmitriy789 [7]
7383829bshsbnebsbbwben
4 0
3 years ago
How to draw a plane that contains A, D, and C
Goryan [66]
Hmm I'm sorry ill keep on trying but can you help me?
4 0
3 years ago
32 students needs 83 mL of acid. How many 1 L bottles of acid needed to be ordered
zimovet [89]
32(83ml)(L/1000ml)=2.656L

Assuming that you can only order integer values, ie not partial bottles, you will need three bottles of acid.
7 0
3 years ago
Other questions:
  • Which equation is not equivalent to the formula m = ca?
    15·1 answer
  • Janet wants to solve the equation above, what should she multiply by both sides of this equation by
    12·2 answers
  • Convert 5 feet to inches .There are 12inches in 1 foot
    11·2 answers
  • Which algebraic expression represents this word description?
    5·1 answer
  • What expression is equivalent to the expression 5 + 3y + 5y?
    11·2 answers
  • Alex wants to test the reliability of “lie detector tests,” or polygraph tests. He performs a polygraph test on a random sample
    6·1 answer
  • Let X be the percentage score on a college-entrance exam for students who did not participate in an exam-preparation seminar. X
    14·1 answer
  • How many colours of the alphabet does it take to taste math?<br><br><br> A: Left<br> B: Right
    12·1 answer
  • Find all the missing elements:
    12·2 answers
  • Where does the line y=2x-12 cross the x-axis?
    14·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!