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bixtya [17]
3 years ago
6

. Compute the required sample size given the required confidence in the sample results is 99.74% (Z score of 3). The level of al

lowable sampling error is 5% and the estimated population standard deviation is unknown. Q/A6.1. Compute the required sample size given the required confidence in the sample results is 99.74% (Z score of 3). The level of allowable sampling error is 5% and the estimated population standard deviation is unknown.
Mathematics
1 answer:
Shtirlitz [24]3 years ago
6 0

Answer:

900 sample size

Step-by-step explanation:

To determine the sample size for a proportion, the margin of error formula is used to determine this:

E=Z_{\frac{\alpha}{2} }*\sqrt{\frac{\hat p \hat q}{{n} }

n=\hat p \hat q*(\frac{Z_{\frac{\alpha}{2} }}{E} )^2

Where p is the proportion, E is the margin of error, n is the sample size, q = 1 - p, Z_\frac{\alpha }{2} is the z score.

Since the proportion is not known, the sample size needed to guarantee the confidence interval and error is at p = 0.5 and q = 1 - p = 1 - 0.5 = 0.5

E = 5% = 0.05, Z_\frac{\alpha }{2} = 3. Hence:

n=0.5*0.5*(\frac{3}{0.05} )^2\\\\n = 900

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Hey!



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<em>Original Equation :</em>

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<em>New Equation {Converted Mixed Numbers Into Improper Fractions} :</em>

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<em>New Solution {Converted to a Mixed Number} :</em>

22\frac{3}{16}


Since the fraction cannot be simplified anymore, this should be our final answer.

<em>So, this means that the answer to the equation is </em> 22\frac{3}{16}.


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