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. 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. 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.

Sagot :

raphealnwobi

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:

[tex]E=Z_{\frac{\alpha}{2} }*\sqrt{\frac{\hat p \hat q}{{n} }[/tex]

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

Where p is the proportion, E is the margin of error, n is the sample size, q = 1 - p, [tex]Z_\frac{\alpha }{2}[/tex] 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, [tex]Z_\frac{\alpha }{2}[/tex] = 3. Hence:

[tex]n=0.5*0.5*(\frac{3}{0.05} )^2\\\\n = 900[/tex]

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