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
Alborosie
3 years ago
10

A study was conducted to determine the proportion of people who dream in black and white instead of color. Among 290 people over

the age of 55, 68 dream in black and white and among 288 people under the age of 25, 19 dream in black and white. Use a 0.05 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 underIdentify the test statistic?Identify the p value?Test the claim by constructing an appropriate confidence level?What is the conclusion base on the hypothesis test?What is the conclusion base on the confidence level?
Mathematics
1 answer:
Mrac [35]3 years ago
7 0

Answer:

he proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

Step-by-step explanation:

In this case we need to determine if the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The hypothesis can be defined as follows:  

<em>H</em>₀: The proportion of people over 55 who dream in black and white is not greater than the proportion of those under, i.e. <em>p</em>₁ - <em>p</em>₂ ≤ 0.  

<em>Hₐ</em>: The proportion of people over 55 who dream in black and white is greater than the proportion of those under, i.e. <em>p</em>₁ - <em>p</em>₂ > 0.  

The information provided is:

n₁ = 290

n₂ = 288

X₁ = 68

X₂ = 19

Compute the sample proportions and total proportions as follows:

 \hat p_{1}=\frac{X_{1}}{n_{1}}=\frac{68}{290}=0.235\\\\\hat p_{2}=\frac{X_{2}}{n_{1}}=\frac{19}{288}=0.066\\\\\hat P=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{68+19}{290+288}=0.151

Compute the test statistic value as follows:

 z=\frac{\hat p_{1}-\hat p_{2}}{\sqrt{\hat P(1-\hat P)[\frac{1}{n_{1}}+\frac{1}{n_{2}}]}}

    =\frac{0.235-0.066}{\sqrt{0.151(1-0.151)[\frac{1}{290}+\frac{1}{288}]}}\\\\=5.67

The test statistic value is 5.67.

The decision rule is:

The null hypothesis will be rejected if the p-value of the test is less than the significance level.

Compute the p-value as follows:

 p-value=P(Z>5.67)\\=1-P(Z

The p-value of the test is quite small.

The null hypothesis will be rejected at 5% significance level.

Thus, the proportion of people over 55 who dream in black and white is greater than the proportion of those under.

The significance level of the test is 5%.

Then the confidence level will be:

Confidence level = 100% - Significance level

                             = 100% - 5%

                             = 95%

Compute the 95% confidence interval for the difference between proportions as follows:

CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}

The critical value of <em>z</em> for 95% confidence level is <em>z</em> = 1.96.

CI=(\hat p_{1}-\hat p_{2})\pm z_{\alpha/2}\cdot\sqrt{\frac{\hat p_{1}(1-\hat p{1})}{n_{1}}+\frac{\hat p_{2}(1-\hat p{2})}{n_{2}}}

      =(0.235-0.066)\pm1.96\cdot\sqrt{\frac{0.235(1-0.235)}{290}+\frac{0.066(1-0.066)}{288}}\\\\=0.169\pm 0.057\\\\=(0.112, 0.226)

The null hypothesis would be rejected if the null value, i.e. (<em>p</em>₁ - <em>p</em>₂) ≤ 0 is not contained in the interval.

The 95% confidence interval consist of values greater than 0.

Thus, the null hypothesis will be rejected.

Concluding that the proportion of people over 55 who dream in black and white lies in the range (0.112, 0.226).

You might be interested in
9. What is the formula to find the sum of the interior angles for any polygon?
SOVA2 [1]

polygon: (n-2) × 180

n: nonagon

octagon has 8 sides

3 0
3 years ago
HELP!!!!! Explain how to solve 7x−3 = 26 using the change of base formula. Include the solution for x in your answer. Round your
DiKsa [7]
26-3=7x (23)
23 divided by 7 =3.2857 (x)
6 0
2 years ago
Maria had planned to walk 10 1/8 miles on wednesday, if she walked 7 2/8 miles in the morning how far would she need to walk in
Ugo [173]

Answer:

Distance Maria had to walk in the afternoon is 2\frac{7}{8}

Step-by-step explanation:

Lets take that Maria walked x miles in the afternoon.

Distance walked in the morning + distance walked in the afternoon = 10\frac{1}{8}

⇒7\frac{2}{8} +x=10\frac{1}{8}

\frac{58}{8} +\frac{8x}{8} =\frac{81}{8}

\frac{58+8x}{8} =\frac{81}{8}

58+8x=81

8x=81-58\\

8x=23

x=\frac{23}{8}

x=2\frac{7}{8}

7 0
3 years ago
Which correlation coefficient represents a moderate negative correlation? r = –0.04 r = –0.24 r = –0.64 r = –0.94
fomenos

The correlation coefficient is a number that indicates the direction

and closeness of points of a line of best of fit.

So it tells us two things.

It tells us the direction of the line of best fit

and it tells us the closeness of the points.

Usually, anything between -0.9 and -0.6 has a moderate negative correlation. If you look at this on a graph, you will notice that the points definitely resemble a line so we say it's moderate.

It will be a negative correlation because the slope is negative.

5 0
3 years ago
Read 2 more answers
A rope of length 18 feet is arranged in the shape of a sector of a circle with central angle O radians, as shown in the
creativ13 [48]

Answer:

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

Step-by-step explanation:

The picture of the question in the attached figure

step 1

Let

r ---> the radius of the sector

s ---> the arc length of sector

Find the radius r

we know that

2r+s=18

s=r \theta

2r+r \theta=18

solve for r

r=\frac{18}{2+\theta}

step 2

Find the value of s

s=r \theta

substitute the value of r

s=\frac{18}{2+\theta}\theta

step 3

we know that

The area of complete circle is equal to

A=\pi r^{2}

The complete circle subtends a central angle of 2π radians

so

using proportion find the area of the sector by a central angle of angle theta

Let

A ---> the area of sector with central angle theta

\frac{\pi r^{2} }{2\pi}=\frac{A}{\theta} \\\\A=\frac{r^2\theta}{2}

substitute the value of r

A=\frac{(\frac{18}{2+\theta})^2\theta}{2}

A=\frac{162 \theta}{(\theta+2)^2}

Convert to function notation

A(\theta)=\frac{162 \theta}{(\theta+2)^2}

6 0
3 years ago
Other questions:
  • Question 1
    8·1 answer
  • I don’t understand how to do this? please help
    14·1 answer
  • What is the surface area of the prism?
    5·1 answer
  • What is the sum of the 12th square number and the 10th square number?
    15·1 answer
  • Brendan throws a rock into a pond. The bottom of the pond is -12.6 ft from the surface of the pond. Brendan is on a patio that i
    13·1 answer
  • Whats the best book ever your opinion
    10·2 answers
  • Please help me out guys, Thank you.<br><br>I am very poor at mathematics​
    5·1 answer
  • 2x+8 find x<br> pleaaasee hurry i need help
    7·2 answers
  • What is <br> 2 (3x+7) = 4
    7·2 answers
  • 15 - (7 - 6)4 * 4 + 9
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!