In: Statistics and Probability
At the beginning of the Summer 2018 semester, a sample of 266 World Campus students were surveyed and asked if they were a first-generation college student. In the sample of 266, 139 said that they were first generation college students. We want to construct a 90% confidence interval to estimate the proportion of all World Campus students who are first generation students. A. In StatKey, construct a bootstrap distribution and use the percentile method to find the 90% confidence interval using the data given. Include a screenshot of your distribution here and clearly identify your confidence interval
.B. Use StatKey or Minitab Express to construct a z distribution to identify the z* multiplier for a 90% confidence interval. Include a screenshot of your distribution here and clearly identify your z* multiplier.
C. Use the formula from the online notes to construct the 90% confidence interval: sample statistic±z^* (standard error). You can use the standard error from the distribution you constructed in part A and the z* multiplier that you found in part B.
The bootstrap distribution for the proprtion of first-generation college student is obtained in statkey by following these steps,
Step 1: Click Bootstrap Confidence Intervals > CI for Single Proportion.
Step 2: Click on Edit data and enter count: 139, sample size: 266 > ok. The screenshot is shoen below,
Step 3: Click on Generate 1000 sample and check box for two-tail. The screenshot is shown below,
(Since the default confidence interval is set for 95%, change the confidence interval by clicking "0.950".)
B)
To construct a z distribution in statkey,
Step 1: Click Theoretical Distribution > Normal.
Step 2: To get 90% confidence interval check box for two tail. The screenshot is shown below,
Now the z multiplier values are,
z = - 1.645 and z = 1.645
C)
From part A,
The screenshot is shoen below,
Edit data Please select values for count and sample size. count: sample size: 266 139 Ok