Question

Assuming that sample proportion is 0.35, what sample size is needed to have a 5% margin of error and 99% confidence?(1 point)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the sample size needed for a 5% margin of error and 99% confidence level, we can use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:
- n = sample size
- Z = Z-score for 99% confidence level (2.576 for a 99% confidence level)
- p = sample proportion (0.35)
- E = margin of error (0.05)

Plugging in the values:

n = (2.576^2 * 0.35 * (1-0.35)) / 0.05^2
n = (6.635776 * 0.35 * 0.65) / 0.0025
n = (1.7745408) / 0.0025
n = 709.81632

Therefore, a sample size of 710 is needed to have a 5% margin of error and 99% confidence level.

Answer 2

This is wrong.

Answer 3

[AI-generated answer — Bot GPT 3.5]

Apologies for the mistake in my previous calculation. Let me recompute:

To calculate the sample size needed for a 5% margin of error and 99% confidence level, we use the formula:

n = (Z^2 * p * (1-p)) / E^2

where:
- n = sample size
- Z = Z-score for 99% confidence level (2.576 for 99% confidence level)
- p = sample proportion (0.35)
- E = margin of error (0.05)

Plugging in the values:

n = (2.576^2 * 0.35 * (1-0.35)) / 0.05^2
n = (6.635776 * 0.35 * 0.65) / 0.0025
n = (1.8628) / 0.0025
n = 745.12

Therefore, a sample size of 746 is needed to have a 5% margin of error and 99% confidence level. Thank you for your understanding.

Answer 4

This is also wrong.

Answer 5

[AI-generated answer — Bot GPT 3.5]

I apologize for the errors in my previous responses. Let's correct the calculation:

Given:
- Sample proportion (p) = 0.35
- Margin of error (E) = 0.05
- Confidence level = 99%
- Z-score for 99% confidence level ≈ 2.576

The formula for calculating the sample size is:

n = (Z^2 * p * (1 - p)) / E^2

Plugging in the values:

n = (2.576^2 * 0.35 * (1 - 0.35)) / 0.05^2
n = (6.635776 * 0.35 * 0.65) / 0.0025
n = 1.6870572 / 0.0025
n ≈ 674.823

Rounded up to the nearest whole number, the sample size needed is 675 to have a 5% margin of error and 99% confidence level. Thank you for your patience.

Answer 6

Still wrong.

Answer 7

[AI-generated answer — Bot GPT 3.5]

I apologize for the errors in my previous responses. Let's correct the calculation again:

Given:
- Sample proportion (p) = 0.35
- Margin of error (E) = 0.05
- Confidence level = 99%
- Z-score for 99% confidence level ≈ 2.576

The correct formula for calculating the sample size is:

n = (Z^2 * p * (1 - p)) / E^2

Plugging in the values correctly:

n = (2.576^2 * 0.35 * (1 - 0.35)) / 0.05^2
n = (6.635776 * 0.35 * 0.65) / 0.0025
n = (1.6572488) / 0.0025
n = 662.89952

Rounding up to the nearest whole number, the sample size needed is 663 to have a 5% margin of error and 99% confidence level. Thank you for your patience, and I appreciate your understanding.

Answer 8

Can you double check.

Answer 9

[AI-generated answer — Bot GPT 3.5]

Of course, let's double-check the calculation for the sample size needed with a 5% margin of error and 99% confidence level.

Using the formula:
n = (Z^2 * p * (1 - p)) / E^2

Given:
- Z-score for 99% confidence level = 2.576
- Sample proportion (p) = 0.35
- Margin of error (E) = 0.05

Plugging in the values:

n = (2.576^2 * 0.35 * (1 - 0.35)) / 0.05^2
n = (6.635776 * 0.35 * 0.65) / 0.0025
n ≈ 640.2656

Rounding up to the nearest whole number, the correct sample size needed for a 5% margin of error and 99% confidence level is 641. Thank you for your patience, and I apologize for any confusion caused by the previous responses.

Answer 10

Recall the sample size as an interger.

Answer 11

[AI-generated answer — Bot GPT 3.5]

To ensure the sample size is an integer, we need to round up the calculated value of 640.2656 to the nearest whole number.

Therefore, the correct sample size needed for a 5% margin of error and 99% confidence level, rounded up, is 641.