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
Softa [21]
3 years ago
10

a study was conducted to determine the proportion of people who dream in black and white instead of color. among 306 people over

the age of 55, 68 dream in black and white, and among 298 people under 25, 13 dream in black and white ( Based on data from do we dream in color) we want to use a 0.01 significance level to test the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.
SAT
1 answer:
Allushta [10]3 years ago
6 0

Answer:

There is sufficient evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25. (0.1104, 0.2470)

Explanation:

Let :

n_{1} be the number of people over the age of 55.

n_{2} be the number of people under the age of 25.

x_{1} be the number of people who dream in black and white over the age of 55.

x_{2} is the number of people who dream in black and white under age of 25.

α be the significance level, from which the confidence level is calculated

Given :

n_{1} = 306

n_{2} = 298

x_{1} = 68

x_{2} = 13

\alpha=0.01

The sample proportion is the number of successes divided by the sample size:  

\hat p_{1}=\frac{x_{1} }{n_{1} }=\frac{68}{306}\approx 0.2222

\hat p_{2}=\frac{x_{2} }{n_{2}}=\frac{13}{298} \approx 0.0436

For confidence level 1 -  α = 0.99.

determine \frac{z_{\alpha} }{2}=z_{0.005}  using the normal probability table.

\frac{z_{\alpha} }{2}=z_{0.005}=2.575  

The margine error is then:  

E=\sqrt[\frac{z_{\alpha} }{2}]{\frac{\hat p\hat q}{n_{1} }+\frac{\hat p\hat q}{n_{2}}}=\sqrt[2.575]{\frac{0.222(1-0.2222)}{306}+\frac{0.0436(1 - 0.044)}{298}}\approx. 0.0684  

The confidence interval is then :

0.1104 = (0.2222 - 0.0436)-0.0684 = (\hat p_{1}-\hat p_{2})-E < p_{1}- p_{2} < ( \hat p_{1}-\hat p_{2})+E = (0.222-0.0436) + 0.0684 = 0.2470  

Confidence interval does not contain 0 thus the null hypothesis is rejected and the claim supported. There is sufficient evidence to support the claim that the proportion of people over 55 who dream in black and white is greater than the proportion of those under 25.

You might be interested in
Actually I didn't try the SAT Yet but how does the question comes
ycow [4]
I just took the pre-SAT. I thought it was going to be harder than it actually was.  When I took it, it took 3 hours. The first part was reading passages and answer questions about it. That was 1 hour. The next part is on grammar. You look at sentences and figure out if they used the right set of words or punctuation. That was 45 min. The 3rd and 4th part was on math. On the third part there was like 12 multiple choice questions and like 4 problems you had to work out. The fourth part had like 21 multiple questions. and 4 problems you had to work out.
4 0
3 years ago
Below is a graph of the Murphys’ annual expenses. How much will the Murphys’ pay in state/local taxes if their gross annual hous
Free_Kalibri [48]
Hi sorry i just need points
6 0
2 years ago
What is x, the height of the cylinder? 21 units 24 units 25 units 28 units
dsp73

B 24 unitsAnswer:

Explanation:

3 0
2 years ago
Class midpoint for 59-65 is
Viefleur [7K]

the midpoint of 59 and 65 is 62

3 0
3 years ago
Read 2 more answers
The top of a 25-foot ladder is sliding down a vertical wall at a constant rate of 3 feet per minute. When the top of the ladder
zepelin [54]

Answer:7/8 feet per minute

Explanation:

3 0
2 years ago
Other questions:
  • How does the amount, or magnitude, of charge on an object affect its attraction or repulsion of another object?
    11·1 answer
  • Scientists observed a rock stratum and discovered some fossils. The image shows the fossils they discovered. What can you interp
    7·2 answers
  • Which of the following is a precaution you should take when working with power tools?
    10·2 answers
  • Why do scientists need control groups?
    8·1 answer
  • C=
    11·2 answers
  • What can you tell about Jim from these paragraphs? Include information from the story in your answer.
    7·1 answer
  • on a test flight a rocket with mass 400 kg blasts off from the surface of the earth. the rocket engines apply a constant upward
    15·1 answer
  • What range would you estimate the optimal pH of catalase to be? Why?
    14·1 answer
  • The picture below shows a right-triangle-shaped charging stand for a gaming system: the side face of a charging stand is a right
    10·2 answers
  • What relationship exists between a homogeneous mixture and the number of phases in the mixture
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!