STAT 2023, Assignment 17, Lesson 16, Inferences on Proportions
A Microsoft Software Testing Facility needed to estimate the proportion lines of code that result in bugs in a beta version of their new Windows System: Windows 10. Suppose they tested 20,000 lines of code in Windows 10 and found 4,400 lines of code result in a bug. Use this information to answer the next 11 questions.
Based on this sample, what is the numerical value of the point estimate for the proportion of lines of code that result in bugs in Windows 10?
What is the numerical value of the estimated standard error for the point estimate for proportion of lines of code that result in bugs in Windows 10? Round your answer to four digits past the decimal.
If the estimated standard error for the point estimate for the proportion of lines of code that result in bugs in Windows 10 is 0.004, what is the bound of error for a 95% confidence interval to estimate the proportion of lines of code that result in bugs in Windows 10?
If the estimated standard error for the point estimate for the proportion of lines of code that result in bugs in Windows 10 is 0.004, what is the 95% confidence interval to estimate the proportion of lines of code that result in bugs in Windows 10 based on these data?
If the estimated standard error for the point estimate for the proportion of lines of code that result in bugs in Windows 10 is 0.004, what is the value of the test statistic to test the hypothesis that the proportion of lines of code that result in bugs in Windows 10 is 0.23?
Assume the test statistic value is -2.5, what is the p-value of the test if the question is, “Do the data support the idea that the proportion is less than 0.23?”
Assume the p-value of the left-tail test described in number 6 is 0.00621. What is the decision at the 1% significance level?
Assume the p-value of the left-tail test described in number 6 is 0.00621. What is the conclusion at the 1% significance level?
Assume the test statistic value is -2.5, what is the p-value of the test if the question is, “Do the data support the idea that the proportion is different from 0.23?”
Assume the p-value of the two-tail test described in number 9 is 0.01242. What is the decision at the 1% significance level?
Assume the p-value of the two-tail test described in number 9 is 0.01242. What is the conclusion at the 1% significance level?
It is believed that 75% of college students have taken out student loans. A sample of 400 students was taken and 328 students said they had taken out student loans. Use this information to answer the next four questions.
Based on this sample what is the numerical value of the point estimate for the proportion of students have taken out student loans?
What is the numerical value of the estimated standard error for the point estimate for the proportion of students have taken out student loans? Round to three digits past the decimal.
Assume that the estimated standard error of the point estimate for the proportion of students who have taken out student loans is 0.07. What is the numerical value of the test statistic to test the hypothesis that more than 75% of students have taken out student loans?
Assume that the estimated standard error of the point estimate for the proportion of students who have taken out student loans is 0.07. What is the bound of error for a 95% confidence interval to estimate the proportion of students who have taken out student loans?
Many public polling agencies conduct surveysto determine the current consumer sentiment concerning the state of the economy. For example, the Bureau of Economic and Business Research (BEBR) at the University of Florida conducts quarterly surveys to gauge consumer sentiment in the Sunshine State. Suppose that BEBR randomly samples 500 consumers and finds that 266 are optimistic about the state of the economy. Use this information to answer the following three questions.
What is the numerical value of the point estimate for the proportion of consumers who are optimistic about the state of the economy?
What is the numerical value of the estimated standard error for the point estimate for the proportion of consumers who are optimistic about the state of the economy? Round to four digits past the decimal.
Assume that the estimated standard error of the point estimate for the proportion of consumers who are optimistic about the state of the economy is 0.04. What is the numerical value of the test statistic to check if the proportion is equal to 50% against an alternative that the proportion is greater than 50%?
