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
spin [16.1K]
3 years ago
12

Q1. (10 points) Suppose we want to estimate the average weight of an adult male in Dekalb County, Georgia. We draw a random samp

le of 1,000 men and weigh them. We find that the average in our sample weighs 180 pounds, and the standard deviation of the sample is 35 pounds. a) Construct a 99% confidence interval for the population mean. b) Interpret your conclusion
Mathematics
1 answer:
netineya [11]3 years ago
8 0

Answer:

a) The 99% confidence interval would be given by (177.144;182.856)

b) We are 99% confident that the true mean for the weight of an adult male in Dekalb County, Georgia is between 177.144 and 182.856.

Step-by-step explanation:

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".

\bar X=180 represent the sample mean

\mu population mean (variable of interest)

s=35 represent the sample standard deviation

n=1000 represent the sample size  

Part a: Confidence interval

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=1000-1=999

Since the Confidence is 0.99 or 99%, the value of \alpha=0.01 and \alpha/2 =0.005, and we can use excel, a calculator or a table to find the critical value. The excel command would be: "=-T.INV(0.005,999)".And we see that t_{\alpha/2}=2.58

Now we have everything in order to replace into formula (1):

180-2.58\frac{35}{\sqrt{1000}}=177.144    

180+2.58\frac{35}{\sqrt{1000}}=182.856    

So on this case the 99% confidence interval would be given by (177.144;182.856)    

Part b

We are 99% confident that the true mean for the weight of an adult male in Dekalb County, Georgia is between 177.144 and 182.856.

You might be interested in
Need help pls will give you a good rating.
Elanso [62]

Answer:

x+4

.....................

5 0
3 years ago
Read 2 more answers
Fencing costs $25.80 per yard. How much does it cost to enclose two adjacent rectangular pastures as shown?
Westkost [7]
13.97 bye








Thank the very best friend and
8 0
3 years ago
Read 2 more answers
What is 9 3/7 in simplest form?
inessss [21]

Answer:

I dont think it can be simplified

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Answer seven and eight please
dimaraw [331]
7.

The slope will be 200 since it increases by two hundred per week

The equation for this would be

y = 200x

8.

J would be the best table
3 0
3 years ago
Please help me asap<br><br>​
dimaraw [331]
Okay so basically 1 + 5 = 180
and if we know 1 = 124 we can assume 5 = 56
and 5 = 4 SOOOO
4 = 56
4 0
3 years ago
Other questions:
  • an integrated circuit voltage of 0.9 volts decreases by 0.2 volts per second how long does it take to reach a voltage of 0.3 vol
    11·1 answer
  • Select the choice which shows all of the diagonals in this polygon and tells how many there are.
    15·2 answers
  • A ball is thrown into the air with an initial velocity of 22 meters per second.The quadratic function h(t)=-4.9t2+22t+5.5represe
    7·1 answer
  • Owens Industries is trying to increase its profile in the community. As part of this effort, Owens sponsors a Little League base
    11·1 answer
  • Marco solves the equation 4sin(3x) + 0.25 ≤ 2sin(3x) − 0.3 by graphing y = 2sin(3x) and y = −0.55. he then locates the intervals
    12·2 answers
  • What is the length of arc S shown below?<br> Enter an exact expression.<br> units
    5·2 answers
  • I can’t use my calculator so can someone please answer 2.8 quintillion to the power of 8 divided by 3.7 billion to the power of
    7·1 answer
  • I am thinking of a number. I subtract 10 then divide by 2 and I now have 19. What was my original number?
    11·2 answers
  • Help what’s the perimeter?
    15·1 answer
  • HELP PLEASEEEEEEEE!!!!!!!
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!