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Rudik [331]
3 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]3 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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michelle bought the same fabric on 3 different occasions and recorded the data below what was the price per yard of fabric? answ
bazaltina [42]

Please consider the complete question.

Michelle bought the same fabric on 3 different occasions and recorded the data below.

Yards of Fabric         Total Cost

2.2                             $2.53

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What was the price per yard of fabric?

To find the cost per yard of fabric, we will divide cost of yards by number of yards.

\text{Cost per yard}=\frac{\text{Cost}}{\text{Number of yards}}

\text{Cost per yard}=\frac{\$2.53}{2.2\text{ yards}}

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Similarly we will find cost per yard for 3rd set of data.

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Therefore, the cost per yard of fabric is $1.15.

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Step-by-step explanation:

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