Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union
Members who favor the Republican candidate.
A) 0.316

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-A survey of 300 union members in New York State reveals that 112 favor the Republican candidate for governor. Construct the 98% confidence interval for the true population proportion of all New York State union
Members who favor the Republican candidate.
A) 0.316 < p < 0.430
B) 0.301 < p < 0.445
C) 0.308 < p < 0.438
D) 0.304 < p < 0.442

Quizplus · Accepted Answer

We can use the formula for confidence interval for population proportion:

point estimate ± z* (standard error)

where point estimate is the sample proportion, z* is the z-score corresponding to the level of confidence (98% in this case), and standard error is:

standard deviation / square root of sample size

Since we do not have any information about the standard deviation of the population, we will use the sample proportion as an estimate for it:

standard deviation ≈ sqrt [p * (1 - p) / n]

Plugging in the values, we get:

point estimate = 112/300 = 0.3733
standard error ≈ sqrt [0.3733 * (1 - 0.3733) / 300] ≈ 0.039

The z-score corresponding to 98% level of confidence is approximately 2.33. Therefore, the confidence interval is:

0.3733 - 2.33(0.039) < p < 0.3733 + 2.33(0.039)

Simplifying:

0.3081 < p < 0.4385

Therefore, the answer is C.

Use the Given Degree of Confidence and Sample Data to Construct