Question

Find the degree of confidence used in constructing the confidence interval 0.523 < p < 0.669 for the population proportion p using sample data with n = 109, x = 65.

a) 90%
b) 99%
c) 95%
d) 88%

Answer 1

The degree of confidence used in constructing the confidence interval is 90%.

The answer is option ⇒a

Step-by-step explanation:

The degree of confidence used in constructing the confidence interval is determined by the z-value. In this case, since the sample data has a sample size of 109 and the confidence interval is 0.523 < p < 0.669, we can calculate the standard error using the formula:

Standard Error = √[(p(1-p))/n]

Using the lower bound value 0.523, we can calculate the standard error as:

Standard Error = √[(0.523(1-0.523))/109]

Then, we can use the z-value to find the corresponding degree of confidence. For example, if we use a z-value of 1.645, which corresponds to a 90% confidence level, the confidence interval would be 0.523 ± (1.645 x Standard Error), which results in a confidence interval of approximately 0.335 to 0.711.

Therefore, the correct answer is a) 90%.