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a_sh-v [17]
3 years ago
12

A simple random sample of 100 8th graders at a large suburban middle school indicated that 81% of them are involved with some ty

pe of after school activity. Find the 98% confidence interval that estimates the proportion of them that are involved in an after school activity.
Mathematics
1 answer:
Sophie [7]3 years ago
4 0

Answer:

The  interval is  0.7187  < p < 2.421

Step-by-step explanation:

From the question we are told that

      The  sample size is  n  = 100

       The  population  proportion is p  =  0.81

       The  confidence level is  C =  98%

The level of significance is mathematically evaluated as

     \alpha  =  100 -98

    \alpha  =  2%%

    \alpha  =  0.02

Here this level of significance represented the left and the right tail

The degree of  freedom is evaluated as

     df =  n-1

substituting value  

    df =  100 - 1

     df = 99

Since we require the critical value of one tail in order to evaluate the  98% confidence interval that estimates the proportion of them that are involved in an after school activity. we will divide the level of significance by 2

The  critical value of  \frac{\alpha}{2} and the evaluated degree of freedom is  

      t_{df , \alpha } =  t_{99 , \frac{0.02}{2}  }  = 2.33

this is obtained from the critical value table  

The standard error is mathematically evaluated as

             SE =  \sqrt{\frac{p(1-p )}{n} }  

substituting value  

           SE =  \sqrt{\frac{0.81(1-0.81 )}{100} }  

           SE = 0.0392  

The 98%  confidence interval is evaluated as

      p  - t_{df ,  \frac{\alpha }{2} } *  SE  < p <  p  + t_{df ,  \frac{\alpha }{2} }

substituting value  

     0.81  - 2.33  *  0.0392  < p <  0.81  +2.33 *  0.0392

      0.7187  < p < 2.421

     

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You should plot the total distance traveled from the base camp on the x-coordinate while the elevation should be plotted on the y-coordinate.

<h3>What is a graph?</h3>

A graph simply refers to a type of chart which is commonly used to graphically represent data on both the vertical and horizontal lines of a cartesian coordinate (x-coordinate and y-coordinate).

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6 0
1 year ago
At the local market, Bill buys 3 juice boxes and 2 hot dogs at a cost of $8, while Sarah buys 2 juice boxes and 1 hot dog at a c
baherus [9]

Answer:

The cost of each juice boxes is $ 2

The cost of each hot dogs is $ 1  .

Step-by-step explanation:

Given as :

The amount which Bill pays for 3 juice boxes and 2 hot dogs = $ 8

The amount which Sarah pays for 2 juice boxes and 1 hot dogs = $ 5

Let The cost of each juice boxes = $ j

And The cost of each hot dogs = $ h

Now, According to question

3 j + 2 h = 8               .........A

2 j + 1 h = 5                 ..........B

Now, solving the equations

2 × (  2 j + 1 h ) = 2 × 5

or, 4 j + 2 h = 10

I.e ( 4 j + 2 h ) - ( 3 j + 2 h ) = 10 - 8

Or, ( 4 j - 3 j ) + ( 2 j - 2 h ) = 2

Or, j + 0 = 2

∴  j = 2

So , The cost of each juice boxes = j = $ 2

Now, Put the value of j in Eq A

I.e  3 × 2 + 2 h = 8

Or, 6 + 2 h = 8

Or. 2 h = 8 - 6

or, 2 h = 2

∴   h = \frac{2}{2} = 1

So, The cost of each hot dogs = h = $ 1

Hence The cost of each juice boxes is $ 2

And The cost of each hot dogs is $ 1  . Answer

4 0
3 years ago
Please help i need it now
Aneli [31]

Answer:

Square root of 36 and square root of 5.

Step-by-step explanation:

You have to put square root of 36 in one box and square root of 5 in the other box.

If this helps please mark as brainliest

3 0
2 years ago
Read 2 more answers
I need help with this please.
SSSSS [86.1K]

Answer:

f )  x+72=90(complementary angle)

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3 years ago
Question 4 (1 point)
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The Answer to your question I believe is False…

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