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SOVA2 [1]
3 years ago
6

A research center project involved a survey of 851 Internet users. It provided a variety of statistics on Internet users. (a) Th

e sample survey showed that 92% of respondents said the Internet has been a good thing for them personally. Develop a 95% confidence interval for the proportion of respondents who say the Internet has been a good thing for them personally. (Round your answers to four decimal places.)
Mathematics
1 answer:
kotykmax [81]3 years ago
8 0

Answer:

The answer is "(0.9193924 , 0.9206076)".

Step-by-step explanation:

\text{sample proportion}\ (SP) = 0.92\\\\\text{sample size}\ n = 851\\\\\text{Standard error} \ SE = \sqrt{\frac{(SP \times(1 - SP)}{n})}\\\\

                              =  \sqrt{\frac{(0.92  \times (0.08)}{851})}\\\\= \sqrt{\frac{0.0736}{851}}\\\\=  \sqrt{8.648\times 10^{-5}}\\\\=0.00031

\text{CI level is}\ 95\% \\\\\therefore\\\\ \alpha = 1 - 0.95 = 0.05\\\\\frac{\alpha}{2} = \frac{0.05}{2} = 0.025\\\\ Z_c = Z_{(\frac{\alpha}{2})} = 1.96

Calculating the Margin of Error:

ME = z_{c} \times SE\\\\

       = 1.96 \times 0.00031\\\\ = 0.0006076

CI = (SP - z*SE, SP + z*SE)

      = (0.92 - 1.96 * 0.00031 , 0.92 + 1.96 * 0.00031)\\\\ = (0.92 - 0.0006076 , 0.92 +  0.0006076)\\\\= (0.9193924 , 0.9206076)

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Which of the following investments could be represented by the function A = 250(1 + 0.08/12)12 × 4?
Alekssandra [29.7K]

hello,

the first term is 250 so this is the initial invested amount

(1+\dfrac{0.08}{12})^{12}=(1+\dfrac{8\%}{12})^{12}

is to compute 8% annual interest compounded monthly (there are 12 months in a year)

and then multiply by 4 means that it is computed for 4 years so

finally the answer is

$250 is invested at 8% annual interest compounded monthly for 4 years

hope this helps

7 0
2 years ago
What is the area of the polygon?
Brilliant_brown [7]

Answer: 810m^{2}

Step-by-step explanation:

First, we divide the composite figure into two distinct geometric shapes. This would be a triangle and a square. To find the triangle we use the formula:

A = 1/2bh

To find the base of the triangle we can add:

9 + 9 + 18 = 36

Now we plug in and solve:

A = 1/2bh

A = 1/2(36)(27)

= 1/2(972)

= 486

To find the square, we can use length x width:

18×18 = 324

Now, we add the sums together:

486 + 324 = 810

5 0
2 years ago
Combine like terms to create an equivalent expression. -2/3p + 1/5 - 1 + 5/6p
Marat540 [252]
Move the expression around so variables are with variables and numbers with numbers: 5/6p-2/3p+1/5-1

create a common denominator for variables and numbers: 5/6p-4/6p+1/5-5/5

simplify: 1/6p-4/5
5 0
3 years ago
Read 2 more answers
The measures of the angles in △ABC are given by the expressions in the table.
spayn [35]

Answer:

Part 1) x=25

Part 2) m\angle B=65^o

Part 3) m\angle C=50^o

Step-by-step explanation:

step 1

Find the value of x

we know that

The sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle ABC

m\angle A+m\angle B+m\angle C=180^o

substitute the given values

65^o+(3x-10)^o+(2x)^o=180^o

Solve for x

(5x+55)^o=180^o

5x=180-55\\5x=125\\x=25

step 2

Find the measure of angle B

we know that

m\angle B=(3x-10)^o

substitute the value of x

m\angle B=(3(25)-10)=65^o

step 3

Find the measure of angle C

we know that

m\angle C=(2x)^o

substitute the value of x

4 0
3 years ago
Read 2 more answers
The resting heart rate of US females 20 years old or older is normally distributed with a mean of 75 bpm (beats per minute). Sup
Sergio [31]

Answer:

69 bpm

Step-by-step explanation:

Here we start out finding the z-score corresponding to the bottom 33% of the area under the standard normal curve.  Using the invNorm( function on a basic TI-83 Plus calculator, I found that the z-score associated with the upper end of the bottom 33% is -0.43073.

Next we use the formula for z score to determine the x value representing this woman's heart rate:

       x - mean                              x - 75 bpm

z = ----------------- = -0.43073 = --------------------

       std. dev.                                    15

Thus,  x - 75 = -0.43073(15) = -6.461, so x = 75 - 6.6461, or approx. 68.54, or (to the nearest integer), approx 69 bpm

7 0
3 years ago
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