Question

) In a locality of 18000 families a sample of 840 families was selected, of these 840 families, 206 families were found to have a monthly income of Ksh7000 or less. It is desired to estimate how many out of the 18000 families have a monthly income of Ksh3000 or less. Within what limits would you place your estimate

Answer 1

Explanation:

Percentage of families that have income as 500 or less are 20% and 28%.

Let the proportion of families that have income as 500 or less be = p

Thus,

p = \dfrac{x}{n} = \dfrac{206}{840} = 0.24p=nx=840206=0.24

q = 1-p = 1 - 0.24 = 0.75q=1−p=1−0.24=0.75

Therefore,

Expected number of families that have income as 500 or less = 18000 × p

= 18000 × 0.24 = 4410=18000×0.24=4410

\text{ S.e of p} =\dfrac{p(1-p)}{n} =\dfrac{ 0.24 \times 0.75 }{ 840} = 0.014 S.e of p=np(1−p)=8400.24×0.75=0.014

Thus, the most probable limit for p will be - 0.24 + 3 ( 0.014)0.24+3(0.014)

- 0.200 \text{ and } 0.289−0.200 and 0.289

Therefore, the percentage of families that have income as 500 or less are 20% and 28%.

Answer 2

Answer:

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