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
lorasvet [3.4K]
3 years ago
12

To estimate the percentage of a state's voters who support the current

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0

Answer:

The Herald's estimate is likely closest to the actual  percentage of voters who support the governor for reelection.

Step-by-step explanation:

The law of large numbers, in probability concept, states that as we increase the sample size, the mean of the sample (\bar x) approaches the whole population mean (\mu).

That is, as <em>n</em> → ∞, \bar x → \mu.

In this case we are estimating the  percentage of a state's voters who support the current governor for reelection.

A Normal approximation to binomial can be applied to approximate the distribution of <em>p</em> if the following conditions are satisfied:

  • n\hat p \geq  10
  • n (1-\hat p) \geq  10

The sample selected by all the three newspaper are quite large.

Check if Normal approximation to binomial can be applied to approximate the distribution of <em>p</em> for all three.

  • For <em>n</em> = 1000 and \hat p = 0.61 check the conditions as follows:

       n\hat p=1000\times 0.61=610>10\\n(1-\hat p)=1000\times (1-0.61)=390>10\\

       Thus, p\sim N(n\hat p,n\hat p(1-\hat p))=N(610, 237.9).

  • For <em>n</em> = 800 and \hat p = 0.57 check the conditions as follows:

       n\hat p=800\times 0.57=456>10\\n(1-\hat p)=800\times (1-0.57)=344>10\\

       Thus, p\sim N(n\hat p,n\hat p(1-\hat p))=N(456, 196.08)

  • For <em>n</em> = 600 and \hat p = 0.71 check the conditions as follows:

       n\hat p=600\times 0.71=426>10\\n(1-\hat p)=600\times (1-0.71)=174>10\\

       Thus, p\sim N(n\hat p,n\hat p(1-\hat p))=N(426, 123.54)

So, for all the three sample, the proportions follows a Normal distribution.

Now, according to the law of large numbers, as the sample size increases the sample mean approaches the population mean. In case of proportions, the sample mean is the sample proportion itself.

So, as the sample size increases the sample proportions approaches the true proportion value.

The Herald has the largest sample size, i.e. <em>n</em> = 1000, so their estimate of the percentage of voters in their  sample who support the governor would closest to the actual percentage.

Thus, The Herald's estimate is likely closest to the actual  percentage of voters who support the governor for reelection.  

You might be interested in
DUDE IM GETTING MAD BECAUSE I KEEP FORGETTING THE IMAGE AND OMG PLEASE ANSWER IM BEGGING PLS
WITCHER [35]

Let

x = number of tickets

y = cost

For each row, divide the cost over the number of tickets

Row one:  y/x = 3/2 = 1.5

Row two: y/x = 6/4 = 1.5

Row three: y/x = 9/6 = 1.5

Row four: y/x = 12/8 = 1.5

Row five: y/x = 15/10 = 1.5

The constant of proportionality is 1.5

This means each ticket costs $1.50

7 0
3 years ago
Graph the solution set 2(x-y)&gt;6-y
Greeley [361]

Answer:

The area right side to the line

Step-by-step explanation:

2 (X-Y) > 6-Y

2X - 2Y > 6 - Y

2X -6 > Y

Y < 2X - 6

8 0
3 years ago
How many milligrams are equal to 200 grams?
lora16 [44]
200,000 milligrams is equivalent to 200 grams.
4 0
3 years ago
Read 2 more answers
How do I convert 12mi/hr = ? Ft/hr
Blizzard [7]
One mile equals 5,280 feet, therefore you would multiply 12 x 5,280 which is 63360 feet per hour.
5 0
2 years ago
There are three nursing positions to be filled at Lilly Hospital. Position 1 is the day nursing supervisor; position 2 is the ni
Alex Ar [27]

Step-by-step explanation:

Applicants can be filled by equal numbers thus 5 applicants can cover per shift

5 0
3 years ago
Other questions:
  • 7hrs 15min -3hr 55 min
    14·1 answer
  • What is the area of the trapezoid? [A = <br> 1<br> 2<br> (b1 + b2)h]
    10·1 answer
  • I will mark you as brainlinest for correct answer!!!!!pleaseeeee help!!!!!!
    9·1 answer
  • Please help! This has to be a fraction of some sort, but the one I tried did not work, so I’d really appreciate some help.
    14·1 answer
  • Aldo buys candy that costs $6 per pound. He will buy at most 9 pounds of candy. What are the possible amounts he will spend on c
    7·1 answer
  • It is recommended that adults get 8 hours of sleep each night. A researcher hypothesized college students got less than the reco
    7·1 answer
  • a bag contains 10 black tiles and 10 white tiles. caden will randomly select on tile from the bag. what’s the probability caden
    8·1 answer
  • 248 miles per hour = meters per second
    8·2 answers
  • Multiply<br> -9w(-3w^8)<br> Simplify
    12·1 answer
  • Help with math please!!
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!