Question

Information about the proportion of a sample that agrees with a certain statement is given below. Use StatKey or other technology to estimate the standard error from a bootstrap distribution generated from the sample. Then use the standard error to give a confidence interval for the proportion of the population to agree with the statement. StatKey tip: Use "CI for Single Proportion" and then "Edit Data" to enter the sample information. Click here to access StatKey. In a random sample of 400 people, 112 agree and 288 disagree. Estimate the standard error using 1000 samples.

Answer 1

Answer is given below.

Explanation:

Number of people, n = 400

Number of people who agree with the statement is 112.

Number of people who disagree with the statement is 288

Using Stat Key, follow the steps below to obtain the 95% confidence interval for the

proportion of the population to agree with the statement.

1) Open

2) Click on CI for single proportion.

3) Click Edit data key.

4) Enter 112 in count text box.

5) Enter 400 in Sample size text box.

6) Click two-tail.

7) Click Generate 1000 samples key.

Output: (See Image).

Original Sample

Count SampleSize Proportion

112 400 0.280

Bootstrap Sample

Count SampleSize Proportion

128 400 0.320

From the above dot plot , it can be observed that the standard error shows top right corner.

Thus the standard error is 0.022.

From the output, the 95% confidence interval is 0.2371 to 0.325