Stats Help Stats Help I want to find out the average number

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Stats Help!

I want to find out the average number of people per household in the US. I survery a simple random sample of US households and obtain the results displayed in the following table.

Household Size / Number of households

1 l 27

2 l 34

3 l 16

4 l 13

5 l 6

6 l 3

7 l 1

a) Lacking any other information, our best estimate for the population mean houshold size is the sample mean. What is the sample mean of our data?

b) What is our estimate for the standard deviation of household sizes?

c) What is the estimated standard error of the sample mean? (That is, based on our answer to b, what is our estimate for the standard deviation of the distribution of the sample mean?)

d)Our eeor is the difference between the sample mean and the population mena. Using the normal distribution, find the approximate probability that the absolute value of the error in a survey of this form and size is less than 0.5

e) Can we be reasonably sure that the average household size for all U.S households is between 2 and 3? (Why?)

Solution

Consider the table:

a)

Thus,  
  
Mean = Sum(xf) / Sum(f) =    2.5 [ANSWER]

b)

Here,

Variance = [Sum(x^2f) - Sum(xf)^2/Sum(f)]/[Sum(f)-1] =    1.98989899

Thus,

Standard deviation = sqrt(Variance) =    1.410637795 [ANSWER]

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c)

c)

standard error = s / sqrt(n) = 1.410637795/sqrt(100)

standard error = 0.1410637795 [ANSWER]

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