3 years ago

Please help me please

Mathematics

1 answer:

Volgvan3 years ago

3 0

The answer is 1.29k = t

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Find the minimum sample size needed to estimate the percentage of Democrats who have a sibling. Use a 0.1 margin of error, use a

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Answer:

The minimum sample size is $n =135$

Step-by-step explanation:

From the question we are told that

The confidence interval is $( lower \ limit = \ 0.44,\ \ \ upper \ limit = \ 0.51)$

The margin of error is $E = 0.1$

Generally the sample proportion can be mathematically evaluated as

$\r p = \frac{ upper \ limit + lower \ limit }{2}$

$\r p = \frac{ 0.51 + 0.44}{2}$

$\r p = 0.475$

Given that the confidence level is 98% then the level of significance can be mathematically evaluated as

$\alpha = 100 - 98$

$\alpha = 2\%$

$\alpha =0.02$

Next we obtain the critical value of $\frac{\alpha }{2}$ from the normal distribution table

The value is

$Z_{\frac{\alpha }{2} } = 2.33$

Generally the minimum sample size is evaluated as

$n =[ \frac { Z_{\frac{\alpha }{2} }}{E} ]^2 * \r p (1- \r p )$

$n =[ \frac { 2.33}{0.1} ]^2 * 0.475(1- 0.475 )$

$n =135$

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