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.)

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

joaobezerra joaobezerra · Answer 2 · 2021-11-18T12:24:12+01:00

Using confidence interval concepts, it is found that:

a) As the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 95%.

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 2 standard errors from the population proportion.

Item a:

For a x% confidence interval, approximately x% of confidence intervals will include the population proportion, and this percentage approaches x as the number of intervals increase, hence, the correct sentence is:

As the number of samples increases, the proportion of 95% confidence intervals that include the population proportion approaches 95%.

Item b:

By the Empirical Rule, 95% of the measures are within 2 standard deviations of the mean, hence, the correct sentence is:

If a 95% confidence interval results in a sample proportion that does not include the population proportion, then the sample proportion is more than 2 standard errors from the population proportion.

A similar problem is given at https://brainly.com/question/23536238