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
13

In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear pow

er plant, it is found that 63 of 100 urban residents favor the construction while only 59 of 125 suburban residents are in favor. We wish to know if there a significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant. Do the step by step procedure on hypothesis test of two proportions, use 0.05 level.
Mathematics
1 answer:
leva [86]3 years ago
8 0

Answer:

The test statistic z = z = 2.368 >1.97 (at 5% level of significance)

we rejected null hypothesis at 5% level of significance

There is  significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

Step-by-step explanation:

Given data In a study to estimate the proportion of residents in a certain city and its suburbs who favor the construction of a nuclear power plant, it is found that 63 of 100 urban residents

The first sample proportion  p₁ = \frac{63}{100} =0.63

The construction of  59 of 125 suburban residents are in favor

The second  sample proportion p_{2} = \frac{59}{125}  = 0.472

Given the sample sizes are n₁ = 100 and n₂ =125

<u>Null hypothesis(H₀):</u>-there is no significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

<u>Alternative hypothesis: H₁</u>

There is  significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

<u>Level of significance</u>:-

∝ =0.05

Tabulated value z=1.96

<u>Test statistic</u>

<u></u>z = \frac{p_{1}-p_{2}  }{\sqrt{pq(\frac{1}{n_{1} } +\frac{1}{n_{2} } )} }<u></u>

where p = \frac{n_{1}p_{1} +n_{2}p_{2}  }{n_{1} +n_{2} }         q = 1- p

Substitute all values in above equation

p = \frac{100X0.63+0.472X125}{100+125} = 0.542

q = 1-p = 1 - 0.542 = 0.458

The test statistic

z = \frac{0.63-0.472}{\sqrt{0.542X0.458}(\frac{1}{100}+\frac{1}{125}   )}

on simplification , we get

z = 2.368 >1.97 (at 5% level of significance)

we rejected null hypothesis at 5% level of significance

<u>Conclusion</u>:-

There is  significant difference between the proportions of urban and suburban residents who favor construction of the nuclear plant.

You might be interested in
Compare and Contrast Graph y = 2x + 5 and y=-13x+5. Describe how these lines are alike and how they are different. *​
krek1111 [17]

Here are a couple I found:

<u>Similarities</u>:

  • They have the same y-intercept of (0,5).
  • They are both in slope-intercept form.

<u>Differences</u>:

  • The line of y = -13x + 5 "falls" from left to right. The line of y = 2x + 5 "rises" from left to right.
  • They have different x-intercepts. (y = 2x + 5 intersects (-\frac{5}{2}, 0) while y = -13x + 5 intersects at (\frac{5}{13}, 0)

<u></u>

<u>Explanation</u>:

Slope-intercept form is y = mx + b, and by looking at the equations, they both already fit that format, with m as their slope and b as their y-intercept. Also, since they both have a 5 as that "b," their y-intercepts are the same: (0,5).

As for differences, we can see that the coefficient in place of that "m" is positive in y = <u>2x</u> + 5 and negative in y = <u>-13x</u> + 5. Therefore, one line would rise due to their slope being positive and one would fall due to their slope being negative. They also have two different x-intercepts, which we can calculate by substituting 0 in place of the y, then isolating x.

4 0
2 years ago
Aaron found rhe length of the diagonal of a rectangle to be an irrational number. What could be the lenght of the diagonal
Amanda [17]

Answer:

See below

Step-by-step explanation:

It could be a positive square root l like √10  ( the number not being a perfect square).

He would have obtained this value from the application of the Pythagoras theorem. For example the length and width of the rectangle might have been 3 and 1 foot respectively, so the diagonal would have length  √(3^2 + 1^2) = √10.

He could give an estimate of the length to nearest hundredth using his calculator. This would be 3.16 feet.

7 0
3 years ago
Review the table.
Lynna [10]

Answer:

The function that models the scenario is given as follows;

P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}

Step-by-step explanation:

The table of values are presented as follows;

The number of days, t, since the rumor started: 0, 1, 2, 3, 4, 5

The number of people, P, hearing the rumor: 10, 16, 26, 42, 66, 100

Imputing the given functions from the options into Microsoft Excel, and

A = P(t) = \dfrac{250}{1 + 24 \cdot e^{-0.5 \cdot t}}

B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}}

C = P(t) = \dfrac{750}{1 + 74 \cdot e^{-0.5 \cdot t}}

D = P(t) = \dfrac{1000}{1 + 99 \cdot e^{-0.5 \cdot t}}

solving using the given values of the variable, t, we have;

P                t               A                 B       {}             C                      D

10        {}      0        {}     10        {}         10        {}          10        {}             10

16        {}      1        {}      16.07021       16.27604      16.34583        {} 16.38095

26        {}     2        {}     25.43466      26.2797       26.574             26.72363

42        {}     3        {}     39.33834      41.89929      42.82868         43.30901

66        {}     4        {}     58.85058      65.51853      68.09014         69.45316

100        {}   5        {}     84.17395        99.55866    106.0177          109.5721

Therefore, by comparison, the function represented by B = P(t) = \dfrac{500}{1 + 49 \cdot e^{-0.5 \cdot t}} most accurately models the scenario.

7 0
3 years ago
Read 2 more answers
Multiply and Simplify. 4x+4/x^2 × (x+2)(x-1)/x+1
NARA [144]

Answer:


Step-by-step explanation:

(x^2 - 4)(x^2 - 4)

Simplifying

(x2 + -4)(x2 + -4)

Reorder the terms:

(-4 + x2)(x2 + -4)

Reorder the terms:

(-4 + x2)(-4 + x2)

Multiply (-4 + x2) * (-4 + x2)

(-4(-4 + x2) + x2(-4 + x2))

((-4 * -4 + x2 * -4) + x2(-4 + x2))

((16 + -4x2) + x2(-4 + x2))

(16 + -4x2 + (-4 * x2 + x2 * x2))

(16 + -4x2 + (-4x2 + x4))

Combine like terms: -4x2 + -4x2 = -8x2

(16 + -8x2 + x4)

5 0
3 years ago
What is the value of x in the equation x + 10 = 13?
ValentinkaMS [17]
The answer is x=3 Your Welcome!
7 0
3 years ago
Read 2 more answers
Other questions:
  • 2x=(360÷4)<br><br> solve for x
    15·2 answers
  • Math help <br> is it D? <br> please and thank you
    5·2 answers
  • What is the relation ship the 6's in 6,600
    9·1 answer
  • How do you make 55 2/3 an answer
    10·2 answers
  • 1. Solve the equation.
    5·1 answer
  • PLZ HELP I ONLY HAVE 11 points left and I need help with this question plz :( It's URGENT
    10·1 answer
  • Plsss help I’ll give u brainlest and 10 points
    11·1 answer
  • For what value of x must ABCD be a parallelogram ?
    15·1 answer
  • Type the expression that results from the following series of steps:
    11·1 answer
  • 16:12 give the answer as n:1
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!