Getting ready for the final, don't understand how to answer these

[chriskeller1]

Please please urgent help needed with questions like these

How do I predict how big the sample needs to be?

View attachment 3688

 

[MarkFL]

Regarding confidence intervals for one mean or proportion, we are given that the maximum error $E$ of the estimate for $\mu$ is:

\(\displaystyle E=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

So, by what factor must $n$ increase so that $E$ is one-fifth as large?

 

[chriskeller1]

Regarding confidence intervals for one mean or proportion, we are given that the maximum error $E$ of the estimate for $\mu$ is:

\(\displaystyle E=z_{\alpha/2}\cdot\frac{\sigma}{\sqrt{n}}\)

So, by what factor must $n$ increase so that $E$ is one-fifth as large?

n must be 5000 right?

 

[MarkFL]

n must be 5000 right?

Yes, because $n$ is under a radical, it must increase by a factor of $5^2=25$ in order for $E$ to be 1/5 as large. and so we find:

\(\displaystyle 200\cdot25=5000\)

 

[CellCoree]

I understand your concern and the importance of preparing for a final exam. Predicting the appropriate sample size is a crucial aspect of conducting scientific research. There are various statistical methods and formulas that can help determine the ideal sample size for a study. Some factors to consider include the research question, the population size, the level of precision desired, and the expected effect size. It is also important to consult with a statistician or use a sample size calculator to ensure accurate results. I recommend reviewing your course materials and consulting with your instructor for additional guidance on how to calculate sample size for your specific exam questions.