Westonci.ca makes finding answers easy, with a community of experts ready to provide you with the information you seek. Connect with professionals on our platform to receive accurate answers to your questions quickly and efficiently. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.

. 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 :

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]