Question

Fill in the blanks to complete the sentences below. (a) As the number of samples​ increases, the proportion of​ 95% confidence intervals that include the population proportion approaches​ ______. (b) If a​ 95% confidence interval results in a sample proportion that does not include the population​ proportion, then the sample proportion is more than​ ______ standard errors from the population proportion. ​(This is a reading assessment question. Be certain of your answer because you only get one attempt on this​ question.)

Answer 1

Answer:

a) the proportion of​ 95% confidence intervals that include the population proportion approaches 0.95

b) Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion

Step-by-step explanation:

a)

Given the the data in the question, confidence level is 95%.

In this case as the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 0.95. hence the expected value of the proportion.

b)

Given the the data in the question, confidence level is 95% and sample proportion

we know that In normal distribution 68% confidence indicate one standard deviation, 95% confidence indicate 2 standard deviation while 99.97% confidence indicate 3 standard deviation.

The sample proportion does not include the population proportion, in 95% confidence from the standard normal table 0.95 value lies within the critical value of 1.96 approximately 2.

hence ( z =2 ) that satisfied the 1.96 standard error from the population proportion

hence, Sample proportion does not include the population proportion then the sample proportion is more than 1.96 standard error from the population proportion