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Rudik [331]
2 years ago
13

In a random sample of 400 residents of Boston, 320 residents indicated that they voted for Obama in the last presidential electi

on. Develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.
Mathematics
1 answer:
coldgirl [10]2 years ago
3 0

Answer:

C.I =  0.7608   ≤ p ≤   0.8392

Step-by-step explanation:

Given that:

Let consider a  random sample n = 400 candidates where  320 residents indicated that they voted for Obama

probability \hat p = \dfrac{320}{400}

= 0.8

Level of significance ∝ = 100 -95%

= 5%

= 0.05

The objective is to  develop a 95% confidence interval estimate for the proportion of all Boston residents who voted for Obama.

The confidence internal can be computed as:

=\hat p  \pm Z_{\alpha/2} \sqrt{\dfrac{ p(1-p)}{n } }

where;

Z_{0.05/2} = Z_{0.025} = 1.960

SO;

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.8(1-0.8)}{400 } }

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.8(0.2)}{400 } }

=0.8  \pm 1.960 \sqrt{\dfrac{ 0.16}{400 } }

=0.8  \pm 1.960 \sqrt{4 \times 10^{-4}}

=0.8  \pm 1.960 \times 0.02}

=0.8  \pm 0.0392

= 0.8 - 0.0392     OR   0.8 + 0.0392  

= 0.7608    OR    0.8392

Thus; C.I =  0.7608   ≤ p ≤   0.8392

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Akimi4 [234]

Answer: (x - 2)² + (y - 14)² = 1

Step-by-step explanation:

<u>Concept:</u>

Here, we need to know the idea of the circle formula.

Circle formula: (x - h)² + (y - k)² = r²

Center = (h, k)

Radius = r

If you are still confused, please refer to the attachment below for a graphical explanation.

<u>Solve:</u>

Center = (2, 14)

Radius = 1

<em>Given formula</em>

(x - h)² + (y - k)² = r²

<em>Substitute the value into the formula</em>

(x - 2)² + (y - 14)² = (1)²

<em>Simplify</em>

(x - 2)² + (y - 14)² = 1

Hope this helps!! :)

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8 0
3 years ago
A chef is going to use a mixture of two brands of Italian dressing. The first brand contains 7% vinegar, and the second brand co
Lina20 [59]

Answer: There is 162 ml of first brand and 108 ml of second brand.

Step-by-step explanation:

Since we have given that

Percentage of vinegar that the first brand contains = 7%

Percentage of vinegar that the second brand contains = 12%

Percentage of vinegar in mixture = 9%

Total amount of dressing = 270 ml

We will use "Mixture and Allegation":

First brand                  Second brand

     7%                                12%

                       9%

--------------------------------------------------------

12%-9%             :                9%-7%

 3%                   :                    2%

So, ratio of first brand to second brand in a mixture is 3:2.

So, Amount of first brand she should use is given by

\dfrac{3}{5}\times 270\\\\=162\ ml

Amount of second brand she should use is given by

\dfrac{2}{5}\times 270\\\\=108\ ml

Hence, there is 162 ml of first brand and 108 ml of second brand.

4 0
3 years ago
When the outliers are removed, how does the mean change? (2 points) dot plot with 1 on 50, 1 on 76, 1 on 78, 2 on 79, 1 on 80, 1
777dan777 [17]

Answer:

Answer: The mean increases by 3

Step-by-step explanation:

The original data set is 

{50, 76, 78, 79, 79, 80, 81, 82, 82, 83}

The outlier is 50 because it is not near the group of values from 76 to 83 which is where the main cluster is.

The original mean is M = (50+76+78+79+79+80+81+82+82+83)/10 = 77

If we take out the outlier 50, the new mean is N = (76+78+79+79+80+81+82+82+83)/9 = 80

So in summary so far

old mean = M = 77

new mean = N = 80

The difference in values is N-M = 80-77 = 3

So that's why the mean increases by 3

8 0
3 years ago
Cory has designed a special table with a circular cutout in the center to be filled with glass. The radius of the cutout is 7 in
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Answer:

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abruzzese [7]

Call the number : x

(1/3)x + 5 = x-6

=> (1/3)x + 5 - (x-6) = 0
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=> [(1/3)x - x] + (5+6) = 0
=> (-2/3)x + 11 = 0
=> (-2/3)x = -11
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Recheck : 1/3 x 33/2 + 5 = 33/6 + 5 = 63/6 = 21/2

33/2 - 21/2 = 12/2 = 6 (21/2 is 6 less than 33/2, satisfied.)

4 0
2 years ago
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