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
What is the length of the arc when the degree measure is 60° and the radius is 7?
shepuryov [24]
Inscribed angle =1/2 arc
4 0
3 years ago
What is the sum of 1/2 + 1/4?<br><br> A. 2/8<br> B. 2/6<br> C. 4/8<br> D. 6/8
Pie

<em>3/4 is the total.</em>

<em></em>

<em></em>

<em>See attached image for explanation.</em>

<em></em>

<em>Please consider marking "Brainliest". </em>

<em></em>

<em>Thanks <3</em>

<em></em>

6 0
2 years ago
What is the domain of the function F(x) = 4 cos(2x+1)?
Veseljchak [2.6K]

Answer:

Domain: (-inf, inf)

Range: [-4,4]

6 0
3 years ago
20) Laila borrowed $9000 from a bank that
iris [78.8K]

Answer:

the answer i think is $259200

Step-by-step explanation:

if the bank charges 7.2% every year, and in this case it's 4 years, then that would mean it would be 28.8%(7.2 x 4), which means the answer would be 9000 x 28.8 which is 259200.

Hope it helped

3 0
3 years ago
Dan paid 34.30 for a sweater. The price included a 40% markup. Find the cost of the sweater before the markup was added.
hodyreva [135]

Answer:

The cost of the sweater before the markup is $24.50.

Step-by-step explanation:

The percent markup of an item is calculated by subtracting the original cost of the item from the sale price and then dividing by the original cost.  In this case, we are trying to find the original cost, so we know that the percent markup is 40%, or 0.4.  Since the sale price of the item would be 100% of the original cost multiplied by an additional 40% markup, we can take the sale price of the item divided by 140%, or 1.4:  34.30/1.4 = 24.50.

7 0
3 years ago
Other questions:
  • Which system is equivalent to<br> y= 9x^2<br> x+y=5<br> ?
    5·2 answers
  • When doing substitution what is the answer for -9x+2y=228, -7x-1=y
    11·2 answers
  • Binomial Distribution Problem 1: (a) An urn contains 1000 balls, 100 are green and 900 are white. One ball is chosen from the ur
    14·1 answer
  • What do the following two equations represent? 4x-2y=-5 and -2x+3y=-3
    7·2 answers
  • Amanda lives in Fairbanks Alaska she records the low temperature for five days, which days low temperature was 9c colder than th
    11·2 answers
  • The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati
    10·1 answer
  • What does 6×3000= equal
    5·2 answers
  • Please answer asap. thank you
    13·2 answers
  • The CD Warehouse is having a clearance sale. A CD player that originally sells for $60 is now priced at $36. What is the percent
    15·1 answer
  • What is the value of x in this triangle?<br> Round only your final answer to the nearest hundredth.
    8·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!