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
bija089 [108]
3 years ago
14

Researchers are interested in the effect of a certain nutrient on the growth rate of plant seeding. Use a hydroponics grow proce

dure that utilized water containing the nutrient, they planted 6 tomato plants and recorded the heights of each plant 14 days after germination. those heights were 54.2, 59.8, 61.8, 63.3, 65.1, 71.4
Use technology, find the 95% confidence interval for the population mean.

use technology, construct a 99% confidence interval.
Mathematics
1 answer:
Rashid [163]3 years ago
8 0

Answer:

The 95% confidence interval for the mean would be given by (56.604;68.596)

The 99% confidence interval for the mean would be given by (53.196;72.004)

Step-by-step explanation:

1) Previous concepts

When we compute a confidence interval for the mean, we are interested on the parameter population mean, and we use the info from the sample to estimate this parameter.

2) Basic operations

The sample mean can be calculated with the following formula

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

Using excel we can use this function to calculate the mean:

=AVERAGE(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is \bar X=62.6

In order to find the sample deviation we can use this formula

s=\sqrt{\sum_{i=1}^n \frac{(x_i-\bar X)^2}{n-1}}

And using excel we can use this function to calculate the sample standard deviation:

=STDEV.S(54.2,59.8,61.8,63.3,65.1,71.4)

The value obtained is s=5.713

The sample size for this case is n=6, n<30 so then is better use the t distribution to calculate the margin of error. First we need to calculate the degrees of freedom, on this case df=n-1=6-1=5

The formula for the confidence interval would be given by:

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

3) Part a

If we want a 95% or 0.95 of confidence, then the value for the signficance is \alpha=1-0.95=0.05, and \alpha/2=0.025, and 1-\frac{\alpha}{2}=0.975 so we can find the critical t value with the following formula in excel:

=T.INV(0.975,5)

And we got t_{\alpha/2}= 2.571

And we can replace into equation (1) and we got:

62.6 \pm 2.571\frac{5.713}{\sqrt{6}}

And using excel with the following formulas we got:

=62.6-2.571*(5.713/SQRT(6)) = 56.604

=62.6+2.571*(5.713/SQRT(6)) = 68.596

So the 95% confidence interval for the mean would be given by (56.604;68.596)

4) Part b

If we want a 99% or 0.99 of confidence, then the value for the signficance is \alpha=1-0.99=0.01, and \alpha/2=0.005, and 1-\frac{\alpha}{2}=0.995 so we can find the critical t value with the following formula in excel:

=T.INV(0.995,5)

And we got t_{\alpha/2}= 4.032

And we can replace into equation (1) and we got:

62.6 \pm 4.032\frac{5.713}{\sqrt{6}}

And using excel with the following formulas we got:

=62.6-4.032*(5.713/SQRT(6)) = 53.196

=62.6+4.032*(5.713/SQRT(6)) = 72.004

So the 99% confidence interval for the mean would be given by (53.196;72.004)

You might be interested in
The scatterplot models the relationship between the length of a Louisiana alligator and the width of the alligators belly.Which
erastovalidia [21]

Answer:

c

Step-by-step explanation:

4 0
3 years ago
Read 2 more answers
What is the final transformation in this sequence of
Serhud [2]

Answer: D - a rotation 180° about Z’

4 0
3 years ago
(1/2)/(2/3) evaluate
nikitadnepr [17]

Answer:

\frac{3}{4}

Step-by-step explanation:

  1. Find a common denominator for the 2 denominators: 6
  2. Change the fractions: 2 × 3 = 6, 1 × 3 = 3, 3 × 2 = 6, 2 × 2 = 4
  3. Re-write the fractions: \frac{3}{6} and \frac{4}{6}  
  4. Write as an expression: \frac{3}{6} ÷ \frac{4}{6}  
  5. \frac{3}{6} ÷ \frac{4}{6} = \frac{3}{6} × \frac{6}{4}
  6. \frac{3}{6} × \frac{6}{4} = \frac{18}{24}  
  7. \frac{18}{24} = \frac{3}{4}  

I hope this helps!

8 0
3 years ago
Need help on b ASAP HELP
maxonik [38]
9w^3 ...........................
3 0
3 years ago
Wich is the set i need u heeeeelp
Karo-lina-s [1.5K]

Answer:

I think that it is  26, 51, 103,

I hope this is correct sorry if I'm wrong

Step-by-step explanation:

you add all of them together and they have to get to 180 so 26+51=77   77+103=180

7 0
3 years ago
Other questions:
  • Help me plz need smart people
    15·2 answers
  • Find the number of meters each runner ran in one second<br><br> 200 meters, 19.30 seconds
    10·1 answer
  • How is the answer 35? How do I get it?
    11·1 answer
  • An adult blue whale can eat about 40 million Krill a day write this number in a scientific notation
    13·2 answers
  • PLEASE HURRY IT'S URGENT!!!!!
    9·2 answers
  • Find the x component of the vector 92.5 m 32.0 degrees
    5·2 answers
  • Simplify the expression: 42 + 8 ÷ 2.
    15·1 answer
  • A<br> is part of a line with one endpoint but goes on<br> forever in the other direction.
    13·1 answer
  • for each line, determine whether the slope is positive, negative, zero or undefined. (this is homework.) ​
    6·2 answers
  • Which theorem proves that the two triangles are congruent?
    15·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!