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
Llana [10]
3 years ago
14

The following data were collected from 12 rain gauges in a park. Build a 95% CI for the mean rainfall at the park.

Mathematics
1 answer:
dybincka [34]3 years ago
8 0

Answer:

Critical values:t_{\alpha/2}=-2.201 t_{1-\alpha/2}=2.201

95% confidence interval would be given by (3.646;4.472)

Step-by-step explanation:

1) Previous concepts

A confidence interval is "a range of values that’s likely to include a population value with a certain degree of confidence. It is often expressed a % whereby a population means lies between an upper and lower interval".

The margin of error is the range of values below and above the sample statistic in a confidence interval.

Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".

The data is:

4.65 3.89 2.73 4.35 3.80 4.86 4.33 4.37 4.76 4.05 3.05 3.87

2) Compute the sample mean and sample standard deviation.

In order to calculate the mean and the sample deviation we need to have on mind the following formulas:  

\bar X= \sum_{i=1}^n \frac{x_i}{n}

s=\sqrt{\frac{\sum_{i=1}^n (x_i-\bar X)}{n-1}}

=AVERAGE(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

On this case the average is \bar X= 4.059

=STDEV.S(4.65,3.89,2.73, 4.35, 3.8, 4.86, 4.33, 4.37, 4.76, 4.05, 3.05, 3.87)

The sample standard deviation obtained was s=0.6503

3) Find the critical value t* Use the formula for a CI to find upper and lower endpoints

In order to find the critical value we need to take in count that our sample size n =12 <30 and on this case we don't know about the population standard deviation, so on this case we need to use the t distribution. Since our interval is at 95% of confidence, our significance level would be given by \alpha=1-0.95=0.05 and \alpha/2 =0.025. The degrees of freedom are given by:

df=n-1=12-1=11

We can find the critical values in excel using the following formulas:

"=T.INV(0.025,11)" for t_{\alpha/2}=-2.201

"=T.INV(1-0.025,11)" for t_{1-\alpha/2}=2.201

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

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

And we can use Excel to calculate the limits for the interval

Lower interval : "=4.059 -2.201*(0.6503/SQRT(12))" =3.646

Upper interval :  "=4.059 +2.201*(0.6503/SQRT(12))" =4.472

So the 95% confidence interval would be given by (3.646;4.472)

You might be interested in
A little boy mass 10kg is placed at a height of 2cm above the ground,what is the potential energy of the boy with reference to t
marin [14]
Potential gravitational energy:

mgh

10kg • 10m/s^2 • 0.02 =

2 Joules
3 0
2 years ago
Aiko types at a rate of 70 words per minute. After typing at the same rate for 3 minutes, he had typed a total of 210 words. Thi
Eddi Din [679]

Answer:

Not sure if this is correct but it should be y=210x-140

Step-by-step explanation:

8 0
2 years ago
Read 2 more answers
Find the area of a rectangle with side lengths 3/5 inch and 5/6 inch
Helga [31]

Answer:

15/30 0r 1/2

Step-by-step explanation:

You multiply the fractions

8 0
2 years ago
Over the course of a lifetime about how much more does a college graduate earn than someone who does not have a college degree
Dmitry [639]
C or 750,000 because lol thats just what it is, you can look it up
4 0
3 years ago
Solve the inequality.<br> 5(w - 3) &lt; 5w + 20
saveliy_v [14]

Answer:

-15 < 20

Step-by-step explanation:

5(w - 3) < 5w + 20

Distribute;

5w - 15 < 5w + 20

Subtract 5w from both sides;

-15 < 20

7 0
2 years ago
Read 2 more answers
Other questions:
  • What is 17.5% as a decimal?
    15·1 answer
  • Which symbol is used to make -6 ? |-8| a true statement?<br>&gt;<br>&lt;<br>=
    5·2 answers
  • For what values of x and y must each figure be a parallelogram?
    15·2 answers
  • An item is regularly priced at $39. Ashley bought it at a discount of 55% off the regular price.
    5·2 answers
  • Round to the nearest ten thousand 13,501
    8·2 answers
  • What is the value of n if 3/5 of n is 12
    7·2 answers
  • 15-2(7 - x) = 7<br>(Multi- step equations)<br>show steps please:)&lt;4​
    5·2 answers
  • Complete each operation question showing all steps, and reduce the final answer to lowest terms (improper fractions do not need
    10·1 answer
  • The length of the floor is 32 m longed than it’s witdth and there is greater than 200 square meters. You will cover the floor co
    6·1 answer
  • What is the value of s?<br> C<br> units<br> 5<br> B<br> 8<br> 15<br> А.<br> D
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!