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
puteri [66]
3 years ago
14

The General Social Survey asked the question: "For how many days during the past30 days was your mental health, which includes s

tress, depression, and problems with emotions, not good?"Based on responses from 1,151 US residents, the survey reported a 95% confidence interval of 3.40 to 4.24days in 2010.
(a) Interpret this interval in context of the data.
(b) What does "95% confident" mean? Explain in the context of the application.
(c) Suppose the researchers think a 99% confidence level would be more appropriate for this interval. Willthis new interval be smaller or wider than the 95% confidence interval?
(d) If a new survey were to be done with 500 Americans, do you think the standard error of the estimatebe larger, smaller, or about the same.
Mathematics
1 answer:
serg [7]3 years ago
4 0

Answer:

a) For this case we can conclude that we are 95% confident that the true mean for the variable of interest is between 3.4 and 4.24 days in the US population.

b) The 95% confident means that if we select 100 different samples and calculate the 95% confidence interval for each sample selected, then we will have approximately 95 out of 100 confidence intervals will contain the true mean for the parameter of interest.

c) If we have the same info but we want more confidence that implies that the confidence interval would be wider, since the margin of error increase with more confidence.

d) Assuming that we have the same confidence level and the value for the deviation not changes. If we see if we decrease the sample size, then the margin of error would be lower since the original sample size was 1151. So then if we use 500 Americans we would have a lower value for the margin of error for this new interval. And then our confidence interval would smaller than the original.  

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".  

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

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

For the 95% confidence interval the value of \alpha=1-0.95=0.05 and \alpha/2=0.025, with that value we can find the quantile required for the interval in the normal standard distribution.

z_{\alpha/2}=1.96

The confidence interval after apply the formulas was (3.40 ,4.24)

Part a

For this case we can conclude that we are 95% confident that the true mean for the variable of interest is between 3.4 and 4.24 days in the US population.

Part b

The 95% confident means that if we select 100 different samples and calculate the 95% confidence interval for each sample selected, then we will have approximately 95 out of 100 confidence intervals will contain the true mean for the parameter of interest.

Part c

If we have the same info but we want more confidence that implies that the confidence interval would be wider, since the margin of erroe increase with more confidence, because the critical value increase.

Part d

We need to take in count that the margin of error is given by:

ME=t_{\alpha/2}\frac{s}{\sqrt{n}}

Assuming that we have the same confidence level and the value for the deviation s not changes. If we see if we decrease the sample size, then the margin of error would be lower since the original sample size was 1151. So then if we use 500 Americans we would have a lower value for the margin of error for this new interval. And then our confidence interval would smaller than the original.  

You might be interested in
Pabalo is training for a race. His goal is to run 8.5 miles over the next 3 days. This distances he ran each day are shown in th
goblinko [34]

Answer:

He ran a total of 8.439 miles. Over the three days he ran less than he needed to for his goal, he has to run 0.061 more miles to gain his goal

Step-by-step explanation:

simple! add all of the data numbers and you get a total of 8.439 miles. He has to run 8.5 miles but he does not reach that. he has to run 0.061 miles to gain his goal (8.5-8.439) I hope this helps! (got here as soon as possible)

6 0
3 years ago
Read 2 more answers
What is 365 + 100? ANSWER FAST!!!
ycow [4]

You line up the numbers shown in the photo, then add each column

3 0
3 years ago
Read 2 more answers
In Spring, Jack trimmed his tree 3 in. Shorter. In the summer he trimmed it 5 more inches. The tree is now 45 in. Tall. How tall
sergejj [24]

Answer: 53 inches

Step-by-step explanation:3+5=8

45+8= 53

7 0
3 years ago
Read 2 more answers
SOMEONE PLEASE HELP ME QUICK WILL GIVE BRAINLIEST
Wittaler [7]

Answer:

IT would be B I believe

Step-by-step explanation:

f(x) = 3x + 391

4 0
3 years ago
Can please answer these 3 questions
kupik [55]
So it would be 32 lol if
6 0
3 years ago
Other questions:
  • Part A: Solve −np − 70 < 40 for n.
    15·1 answer
  • A basketball team scores 37 points in one quarter is the number 37 prime or composite show your work
    12·1 answer
  • Please help me find the inverse
    13·1 answer
  • What is π/6? I don’t know. No calculators!
    12·2 answers
  • On the planet Jupiter, a ball this thrown upward at a velocity at 10m/s. It's height, h(t) meters after t seconds is given by th
    5·1 answer
  • Which of the following is equal to g(x)?<br> A. 1/3 (x)<br> B. (x+3)<br> C. (x) - 3<br> D. (x - 3)
    5·1 answer
  • -4x - y = 24<br> Complete the missing value in the solution to the equation.<br> ( _,8)
    11·1 answer
  • The circle shown has a radius of 4 cm.
    14·1 answer
  • What is the value of k ?
    7·2 answers
  • Help me guys???????????????
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!