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
Anton [14]
2 years ago
11

A pew research Center project on the state of news media showed that the clearest pattern of news audience growth in 2012 came o

n digital platforms. According to pew research data, 39% of Americans get news online or from a mobile device in a typical day. a. Suppose that you take a sample of 100 Americans. If the population proportion of Americans who get news online or from a mobile device in a typical day is 0.39, what is the probability that fewer than 30% in your sample will get news online or from a mobile device in a typical day? b. Suppose that you take a sample of 400 Americans. If the population proportion of Americans who get news online or from a mobile device in a typical day is 0.39, what is the probability that fewer than 30% in your sample will get news online or from a mobile device in a typical day? c. Discuss the effect of sample size on the sampling distribution of the proportion in general and the effect on the probabilities in (a) and (b).
Mathematics
1 answer:
KengaRu [80]2 years ago
6 0

Answer:

Step-by-step explanation:

Given that:

the sample proportion p = 0.39

sample size = 100

Then np = 39

Using normal approximation

The sampling distribution from the sample proportion is approximately normal.

Thus, mean \mu _{\hat p} = p = 0.39

The standard deviation;

\sigma = \sqrt{\dfrac{p(1-p)}{n} }

\sigma = \sqrt{\dfrac{0.39(1-0.39)}{100} }

\sigma = 0.048

The test statistics can be computed as:

Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}

Z = \dfrac{0.3 - 0.39 }{0.0488}

Z = -1. 8 4

From the z - tables;

P (\hat p \le 0.3 ) = P(z \le -1.84)

\mathbf{P (\hat p \le 0.3 ) = 0.0329}

(b)

Here;

the sample proportion = 0.39

the sample size n = 400

Since np = 400 * 0.39 = 156

Thus, using normal approximation.

From the sample proportion, the sampling distribution is approximate to the mean \mu_{\hat p} =  p = 0.39

the standard deviation \sigma_{\hat p} = \sqrt{\dfrac{p(1-p)}{n} }

\sigma_{\hat p} = \sqrt{\dfrac{0.39 (1-0.39)}{400} }

\sigma_{\hat p} =0.0244

The test statistics can be computed as:

Z = \dfrac{{\hat _{p}} - \mu_{_ {\hat p}} }{\sigma_{\hat p}}

Z = \dfrac{0.3 - 0.39 }{0.0244}

Z = -3.69

From the z - tables;

P (\hat p \le 0.3 ) = P(z \le -3.69)

\mathbf{P (\hat p \le 0.3 ) = 0.0001}

(c) The effect of the sample size on the sampling distribution is that:

As sample size builds up, the standard deviation of the sampling distribution decreases.

In addition to that, reduction in the standard deviation resulted in increases in the Z score, and the probability of having a sample proportion  that is less than 30% also decreases.

You might be interested in
Evaluate the expression if m = 3.<br><br> 3m^2<br><br><br> (SHOW YOUR WORK)
iragen [17]

The value of given expression when m = 3 is 27

<h3><u>Solution:</u></h3>

Given expression is 3m^2

We have to evaluate the given expression for m = 3

To find for m is equal to 3, substitute m = 3 in given expression

From given expression,

\rightarrow 3m^2

Plug in m = 3 in above expression

\rightarrow 3(3)^2 ------ eqn 1

We know that,

a^2 can be expanded as,

a^2=a \times a

Applying this in eqn 1, we get

\rightarrow 3(3)^2=3 \times (3 \times 3)

Simplify the above expression

\rightarrow 3(3)^2=3 \times (3 \times 3) = 3 \times 9 = 27

Therefore, for m = 3 we get,

\rightarrow 3(3)^2=27

Thus value of given expression when m = 3 is found

5 0
3 years ago
8(3n + 5) = -32<br> what does n =
olga_2 [115]

Answer: n = -3

Step-by-step explanation:

8(3n + 5) = -32

  • <em>Divide both sides by 8.</em>

(3n + 5) = -4

  • <em>Subtract 5 by both sides.</em>

3n = -4 - 5

3n = -9

  • <em>Divide both sides by 3.</em>

n = -3

8 0
3 years ago
Pythagoras Theorem and Quadratic Equations<br> Solve for x:<br> a= (x-2)<br> b= 9<br> c= (x+1)
Alex_Xolod [135]

Answer:

Step-by-step explanation:

Pythagoras theorem

a^2=b^2+c^2

(x-2)^2=9^2+(x+1)^2

x^2-4x+4=81+x^2+2x+1

Collect like terms

-4x-2x=82-4

-6x=78

x=-13

3 0
3 years ago
Read 2 more answers
5x+25=2x+29 what’s the measures
AysviL [449]

the measures are x=4/3

4 0
3 years ago
Please<br> Help me on question 1 :))
levacccp [35]

9514 1404 393

Answer:

  -2

Step-by-step explanation:

The solution to the system is where the lines cross. The x-coordinate of that point is its horizontal distance from the y-axis.

The solution is (x, y) = (-2, 2). The x-coordinate is -2.

5 0
2 years ago
Other questions:
  • PLEASE HELP ME ON THIS
    11·1 answer
  • Adrian's recipe for raises muffins calls for 1 3/4 cups raisins for one batch of muffins Adrian wants to make 2 1/2 batches of m
    7·1 answer
  • NEED HELP WITH THIS QUESTION! Thank you
    10·2 answers
  • Evaluate the following expression: 2(1,1) -4(0,1). enter your answer as a vector.
    7·2 answers
  • What is 3/5 minus 1/3
    12·1 answer
  • HELP HELP ASAP PLEASE HELP!!
    10·1 answer
  • 1 1/4 divided by 2/3
    14·2 answers
  • HELP PLS<br> Classify the triangle by its angles &amp; sides if ∠A = 85 &amp;
    12·1 answer
  • Aria is buying snacks for a party. She will buy one pizza for $20 and some garlic rolls for $2 each. Write an expression to repr
    7·1 answer
  • Is this true or False? (0,8) is an x-intercept. If False, provide a correction.
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!