Question

For the following scenarios, please tell me what the minimum sample size needed is, rounded up to the nearest integer (e.g., if your answer is 51.3, round it up to 52). Remember that you cannot survey a fraction of a person – it has to be a whole person. If you round down, then you won’t have the minimum amount of precision needed, so you must round up. For the z-scores, refer to table provided

Confidence Level	z-score
90%	1.65
95%	1.96
99%	2.58

You want to do a study to determine what percentage of the population does an annual check-up/physical at the doctors. You want your study to have 95% confidence with a margin of error of 3%, and based on a similar study last year, you think that the percentage will be around 75%.

1. What are the following, in the correct order: MoE, z, and σ/π? (Whether you use σ or π depends on whether you are calculating sample size for a mean or a proportion).

2. Based on your answers in question 1, calculate the minimum sample size needed.

3. Assume that you have never done a similar study and have no idea what the percentage will be for people doing an annual check-up. What value should you assume the percentage is if you need to calculate the minimum sample size needed?

You want to estimate the percentage of households in the RGV that eat at a sit-down/table service restaurant per week. You want a margin of error of 5% and a confidence level of 90% (you don’t care about having high confidence). You have no idea what the true percentage was in the past or around what it will be this year.

4. What are the following, in the correct order: MoE, z, and σ/π?

5. Using the numbers from question 4, please calculate the minimum sample size needed.

6. See what happens to the sample size when you increase the confidence. Recalculate the minimum sample size using 95% confidence instead of 90%.

7. See what happens to the sample size when you increase (widen) the margin of error. Recalculate the minimum sample size using 10% margin of error instead of 5%, using 90% confidence.

You want to do a study to estimate how many minutes (within ± 15 minutes) UTRGV students spend on watching TV programs per week. You want to have a confidence level of 99%, and you estimate the standard deviation to be 40 minutes.

8. What are the following, in the correct order: MoE, z, and σ/π? (Whether you use σ or π depends on whether you are calculating sample size for a mean or a proportion)

9. Based on your answers in question 8, calculate the minimum sample size needed.

10. If you want a smaller margin of error (e.g., 10 minutes), will it increase or decrease the sample size?

Responses should look like the following:

1. Three number responses, representing MoE, z, and σ/π in that order

2. One rounded-up number

3. Percentage or proportion

4. Three number responses, representing MoE, z, and σ/π in that order

5. One rounded-up number

6. One rounded-up number

7. One rounded-up number

8. Three number responses, representing MoE, z, and σ/π in that order

9. One rounded-up number

10. Increase or decrease

Answer 1

1) MoE=0.03,z=1.96 as P(-1.96<Z<1.96)&\pi=0.5

2)n=(z/MoE)^2 *pi*(1-pi)=(1.96/.03)^2*0.5*0.5

       =1067.5

3. As value of is not given we will assume it to be 0.5

4.

5.

6. For 95% z value is 1.96 as

So

Sample size will decrease

7. Now

So

Sample size will decrease

8.

9.

10.

Hence we see sample size will decrease