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
ycow [4]
3 years ago
11

An article reported that for a sample of 52 kitchens with gas cooking appliances monitored during a one-week period, the sample

mean CO2 level (ppm) was 654.16, and the sample standard deviation was 164.55.
a) calculate and interpret a 95% confidence interval for true average CO2 level in the population of all homes from which the sample was selected .

b) Suppose the investigators had made a rough guess of 175 for the value of s before collecting data .What sanple size would be necessary to obtain an interval width of 50 ppm for confidence level of 95% ?
Mathematics
1 answer:
kolbaska11 [484]3 years ago
6 0

Answer:

a) 654.16-2.01\frac{164.55}{\sqrt{52}}=608.29    

654.16+2.01\frac{164.55}{\sqrt{52}}=700.03    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

b) n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189

Step-by-step explanation:

Part a

The confidence interval for the mean is given by the following formula:

\bar X \pm t_{\alpha/2}\frac{s}{\sqrt{n}}   (1)

In order to calculate the critical value t_{\alpha/2} we need to find first the degrees of freedom, given by:

df=n-1=52-1=51

Since the Confidence is 0.95 or 95%, the value of \alpha=0.05 and \alpha/2 =0.025, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.025,51)".And we see that t_{\alpha/2}=2.01

Replacing we got:

654.16-2.01\frac{164.55}{\sqrt{52}}=608.29    

654.16+2.01\frac{164.55}{\sqrt{52}}=700.03    

And we can conclude that we are 95% confident that the true mean of Co2 level is between 608.29 and 700.03 ppm

Part b

The margin of error is given by :

ME=z_{\alpha/2}\frac{\sigma}{\sqrt{n}}    (a)

The desired margin of error is ME =50/2=25 and we are interested in order to find the value of n, if we solve n from equation (a) we got:

n=(\frac{z_{\alpha/2} s}{ME})^2   (b)

The critical value for 95% of confidence interval now can be founded using the normal distribution. And in excel we can use this formla to find it:"=-NORM.INV(0.025;0;1)", and we got z_{\alpha/2}=1.960, and we use an estimator of the population variance the value of 175 replacing into formula (b) we got:

n=(\frac{1.960(175)}{25})^2 =188.23 \approx 189

You might be interested in
if a + b + c = 9 and a square + b square + c square = 35 the find the value of ab + bc + ca .​ I am in need of help
Advocard [28]

a+b+c=9 and a2+b2+c2=35 then by using identity

(a+b+c)2=a2+b2+c2+2ab+2bc+2ca,we get the answer 9x9=35+2(ab+bc+ca)

2(ab+bc+ca)=9x9-35

2(ab+bc+ca) =81-35then we get ab+bc+ca=46/2 so ab+bc+ca=23

8 0
2 years ago
Mr. Vader wasted 1/4of his laundry his son washed 2/5of it how much of the laundry still needs to be washed
Alik [6]
7/20 still needs to be washed.
4 0
2 years ago
If someone can answer this and explain it, I would really appreciate it, thanks.
daser333 [38]

Answer:

x = 13

Step-by-step explanation:

Now since the lines are parrarel, the intersection points are alternate to each other. Therefore, A = B.

Solve:

8x + 2 = 14x - 76

2 + 76 = 6x

78 = 6x

x = 13

8 0
3 years ago
Read 2 more answers
Determine the slope
Delicious77 [7]

Answer:

1/3

Step-by-step explanation:

We use the formula y2-y1/x2-x1. The two points that I would use are (3,-1) and (-3,-3). This means that the equation will be -3--1/-3-3. This is equal to -2/-6. This is also equal to 1/3. Therefore, the slope is 1/3.

If this helps please mark as brainleist

4 0
3 years ago
If 1+4=5 and 2+5=12 and 3+6=21what does 8+11=
creativ13 [48]
12-5=7
21-12=9
x-21=11
21+11=32
x=32
4 0
3 years ago
Other questions:
  • A senha de meu cofre é dada por uma sequência de seis
    9·1 answer
  • Order each set of values from least to greatest. 0.4,5/8,38%
    15·1 answer
  • For which x is f(x)?=_3<br> -7<br> -4<br> 4<br> 5
    7·1 answer
  • Homer's annual salary is $74,308. If he works all 52 weeks a year, how much is he paid each week?
    9·1 answer
  • 1x + 2 - 3 = 8 <br><br><br> what is x?
    6·2 answers
  • What does the word acidic mean in
    5·2 answers
  • In triangle ABC, the measure of angle B is 50 degrees. Give possible values for the measures of angles A and C if ABC was an acu
    11·1 answer
  • a car has 15 gallons of gas in its tank the car travels 35 miles per gallon of gas how much gas does the car used to go 100 mile
    10·1 answer
  • Can you identify a parallel or perpendicular equation and type the correct code?
    10·1 answer
  • if a tree 20 meters tall casts a shadow 30 meters long, what is the angle of elevation from the shadow to the tip of the tree, t
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!