Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-A study involves 607 randomly selected deaths, with 35 of them caused by accidents. Construct a 98% confidence interval for the true percentage of all deaths that are caused by accidents.
A) 3.91%

Question

Use the given degree of confidence and sample data to construct a confidence interval for the population proportion p.
-A study involves 607 randomly selected deaths, with 35 of them caused by accidents. Construct a 98% confidence interval for the true percentage of all deaths that are caused by accidents.
A) 3.91% < p < 7.62%
B) 3.56% < p < 7.97%
C) 4.20% < p < 7.33%
D) 3.33% < p < 8.21%

Quizplus · Accepted Answer

We can use the formula for a confidence interval for a proportion:
p̂ ± z*√(p̂(1-p̂)/n)
where p̂ is the sample proportion, n is the sample size, and z* is the critical value from the standard normal distribution for the given level of confidence.

In this case, p̂ = 35/607 ≈ 0.0577 and n = 607. The critical value for a 98% confidence interval is approximately 2.33 (found using a standard normal distribution table or calculator).

Plugging these values into the formula, we get:
0.0577 ± 2.33*√(0.0577(1-0.0577)/607)
= 0.0577 ± 0.0224

Therefore, the 98% confidence interval is:
0.0353 < p < 0.0801

Converting to a percentage, we get:
3.53% < p < 8.01%

The closest choice to this interval is B: 3.56% < p < 7.97%.

Use the Given Degree of Confidence and Sample Data to Construct