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barxatty [35]
3 years ago
11

According to a survey of 500, the mean income before taxes of consumer units (i.e., households) inthe U.S. was $60,533 with a st

andard error of 717.51. Find the margin of error for constructing a95% confidence interval on the population mean income before taxes of all consumer units in theU.S
Mathematics
1 answer:
ioda3 years ago
3 0

Answer:

The margin of error for constructing a 95% confidence interval on the population mean income before taxes of all consumer units in the U.S is 1406.32.

Step-by-step explanation:

We are given that according to a survey of 500, the mean income before taxes of consumer units (i.e., households) in the U.S. was $60,533 with a standard error of 717.51.

Margin of error tells us that how much our sample mean value deviates from the true population value.

<u></u>

<u>Margin of error is calculated using the following formula;</u>

        Margin of error =  Z_(_\frac{\alpha}{2}_) \times \text{Standard of Error}

where, \alpha = level of significance = 1 - confidence level

                                                    = 1 - 0.95 = 0.05 or 5%

Standard of Error =  \frac{\sigma}{\sqrt{n} } = 717.51

Now, the value of z at 2.5% level of significance (\frac{0.05}{2} =0.025) is given in the z table as 1.96, that means;

            Margin of error =  Z_(_\frac{\alpha}{2}_) \times \text{Standard of Error}

                                      =  1.96 \times 717.51 = 1406.32

Hence, the margin of error for constructing a 95% confidence interval on the population mean income before taxes of all consumer units in the U.S is 1406.32.

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alukav5142 [94]

Answer:

i). 10 levels of the bricks

ii). 320 bricks

Step-by-step explanation:

First level contains number of bricks = 50

Second level will contain = 50 - 4 = 46 bricks

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Therefore, sequence formed for the number of bricks in each level of the wall will be,

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This sequence is an arithmetic sequence having,

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Common difference 'd' = 46 - 50 = (-4)

Last term of the sequence T_{n}= 14

i). Expression representing last term will be,

  T_{n}=a+(n-1)d

  Here T_{n} = nth term

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  n = number of term (Number of level of the wall)

  d = common difference

  By substituting these values in the formula,

  14 = 50 + (n - 1)(-4)

  14 - 50 = (-4)(n - 1)

  -36 = -4(n - 1)

  9 = (n - 1)  

  n = 9 + 1

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   Expression for the sum of an arithmetic sequence is,

   S_n=\frac{n}{2}[2a+(n-1)d]

   S_n=\frac{10}{2}[2\times 50+(10-1)(-4)]

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4 0
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Jennifer’s grandmother buys carrots at the farm stand.She and her 3 grandchildren equally share the carrots. How many kilograms
ohaa [14]

According to picture Jennifer’s grandmother buys = 28 kg of carrots.

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Number of kilograms of carrots are distributed equally.

<u>In order to find the Number of kilograms of carrots are distributed, we need to divide total Kgs of carrots by total number of grandchildrens.</u>

Therefore ,

28 ÷ 3 .

On dividing 28 by 3, we get 7.

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