To construct a 99.5% confidence interval for the population proportion p, we first need to calculate the sample proportion (p̂) and then use the formula for the confidence interval for a proportion.

Step 1: Calculate the sample proportion (p̂)
p̂ = x/n = 52/71 ≈ 0.732

Step 2: Determine the z-score for a 99.5% confidence interval. The z-score for a 99.5% confidence interval is 2.807 (you can find this value in a standard z-table or using a calculator).

Step 3: Use the formula for the confidence interval for a proportion, which is p̂ ± Z * √[(p̂(1 - p̂) / n].

Substituting the values we have:

0.732 ± 2.807 * √[(0.732 * (1 - 0.732) / 71]

After calculating the above expression, you will get the lower and upper limits of the confidence interval. Remember to round your answer to at least three decimal places.

Question

To construct a 99.5% confidence interval for the population proportion p, we first need to calculate the sample proportion (p̂) and then use the formula for the confidence interval for a proportion.

Step 1: Calculate the sample proportion (p̂)
p̂ = x/n = 52/71 ≈ 0.732

Step 2: Determine the z-score for a 99.5% confidence interval. The z-score for a 99.5% confidence interval is 2.807 (you can find this value in a standard z-table or using a calculator).

Step 3: Use the formula for the confidence interval for a proportion, which is p̂ ± Z * √[(p̂(1 - p̂) / n].

Substituting the values we have:

0.732 ± 2.807 * √[(0.732 * (1 - 0.732) / 71]

After calculating the above expression, you will get the lower and upper limits of the confidence interval. Remember to round your answer to at least three decimal places.

Knowee AI · Accepted Answer

To construct a 99.5% confidence interval for the population proportion p, we first need to calculate the sample proportion (p̂) and then use the formula for the confidence interval for a proportion.

Step 1: Calculate the sample proportion (p̂)
p̂ = x/n = 52/71 ≈ 0.732

Step 2: Determine the z-score for a 99.5% confidence interval. The z-score for a 99.5% confidence interval is 2.807 (you can find this value in a standard z-table or using a calculator).

Step 3: Use the formula for the confidence interval for a proportion, which is p̂ ± Z * √[(p̂(1 - p̂) / n].

Substituting the values we have:

0.732 ± 2.807 * √[(0.732 * (1 - 0.732) / 71]

After calculating the above expression, you will get the lower and upper limits of the confidence interval. Remember to round your answer to at least three decimal places.

Use the given data to construct a 99.5% confidence interval for the population proportion p.=x52, =n71Round the answer to at least three decimal places.Theconfidenceintervalis, .

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