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Nady [450]
3 years ago
11

In a survey of 603 adults, 98 said that they regularly lie to people conducting surveys. Create a 99% confidence interval for th

e proportion of adults who regularly lie to people conducting surveys. Use Excel to create the confidence interval, rounding to four decimal places.

Mathematics
1 answer:
marysya [2.9K]3 years ago
5 0

Answer:

The population proportion is estimated to be with 99% confidence within the interval (0.1238, 0.2012).

Step-by-step explanation:

The formula for estimating the population proportion by a confidence interval is given by:

\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}

Where:

\hat{p} is the sample's proportion of success, which in this case is the people that regularly lie during surveys,

z_{\alpha /2} is the critical value needed to find the tails of distribution related to the confidence level,

n is the sample's size.

<u>First</u> we compute the \hat{p} value:

\hat{p}=\frac{successes}{n}=\frac{98}{603}=0.1625

<u>Next</u> we find the z-score at any z-distribution table or app (in this case i've used StatKey):

z_{\alpha /2}=2.576

Now we can replace in the formula with the obtained values to compute the confidence interval:

\hat{p}\pm z_{\alpha /2}\times\sqrt{\frac{\hat{p}\times(1-\hat{p})}{n}}=0.1625\pm 2.576\times\sqrt{\frac{0.1625\times(1-0.1625)}{603}}=(0.1238, 0.2012)

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USPshnik [31]

The row echelon form of the matrix is presented as follows;

\begin{bmatrix}1 &-2  &-5  \\ 0& 1 &  -7\\ 0&0  &1  \\\end{bmatrix}

<h3>What is the row echelon form of a matrix?</h3>

The row echelon form of a matrix has the rows consisting entirely of zeros at the bottom, and the first entry of a row that is not entirely zero is a one.

The given matrix is presented as follows;

\begin{bmatrix}-3 &6  &15  \\ 2& -6 &  4\\ 1&0  &-1  \\\end{bmatrix}

The conditions of a matrix in the row echelon form are as follows;

  1. There are row having nonzero entries above the zero rows.
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  3. The location of the leading one in a nonzero row is to the left of the leading one in the next lower rows.

Dividing Row 1 by -3 gives:

\begin{bmatrix}1 &-2  &-5  \\ 2& -6 &  4\\ 1&0  &-1  \\\end{bmatrix}

Multiplying Row 1 by 2 and subtracting the result from Row 2 gives;

\begin{bmatrix}1 &-2  &-5  \\ 0& -2 &  14\\ 1&0  &-1  \\\end{bmatrix}

Subtracting Row 1 from Row 3 gives;

\begin{bmatrix}1 &-2  &-5  \\ 0& -2 &  14\\ 0&2  &4  \\\end{bmatrix}

Adding Row 2 to Row 3 gives;

\begin{bmatrix}1 &-2  &-5  \\ 0& -2 &  14\\ 0&0  &18  \\\end{bmatrix}

Dividing Row 2 by -2, and Row 3 by 18 gives;

\begin{bmatrix}1 &-2  &-5  \\ 0& 1 &  -7\\ 0&0  &1  \\\end{bmatrix}

The above matrix is in the row echelon form

Learn more about the row echelon form here:

brainly.com/question/14721322

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8 0
1 year ago
I need help 0ls respond ​
STatiana [176]
Hi what’s your question
5 0
3 years ago
COULD SOMEONE WRITE FORMAT THEN WRITE EQUIVALENT FRACTION AND MIXED NUMBER 11.09 21.06 0.06 0.50 6.15 AND 7.41
Igoryamba
I think you mean write in word format so yea

11.09
"Eleven and 9 hundredths"
To convert decimals to fractions first put the decimal over 1, multiply by ten for every number after the decimal point and simplify.

(11.09/1)(10)(10) *Because there are 2 numbers after the . 0 and 9*

1109/100
This will be the most simplified you can get it!
As a mixed number:
11 9/100

Follow these steps for the rest!

21.06
"twenty one and six thousandths"
1053/50
21 3/50

0.06
"six thousandths" or
"zero and six thousandths"
3/50

0.50
"fifty thousandths" or "five tenths" since 0.50=0.5
1/2


6.15
"six and fifteen thousandths"
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6 3/20

7.41
"seven and fourty one thousandths"
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I HOPE THIS HELPS
7 0
3 years ago
Read 2 more answers
Yi Min is a pitcher on her softball team. This season,
almond37 [142]

Answer:

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Step-by-step explanation:

0.8 times 60= 48

4 0
3 years ago
My tens digit is less than 7. I am one away from being a multiple of 5. If you half me you will not get a whole number. Who am I
Len [333]

Answer:

its B.429

Step-by-step explanation:

20<70

429+1=multiple of 5

429÷2=214.5

so the answer is 429

 

6 0
3 years ago
Read 2 more answers
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