Discussion

Confidence Intervals about a Proportion

Each week, you will be asked to respond to the prompt or prompts in the discussion forum. Your initial post should be 75-150 words in length, and is due on Sunday. By Tuesday, you should respond to two additional posts from your peers. 

For the last several weeks, you have been working with this scenario:

ABC Enterprises is a growing company in which employees must frequently travel by car for business a few times each week. Currently, each employee is allotted 30 dollars each travel day to cover all meals. Sales employees often travel in a 1.5-hour radius of the office and frequently have multiple appointments each week. They have complained that that dollar amount for food is not enough, especially on days with multiple meetings. A survey, given by the CEO, was taken to get a sense of what the employees recommended for a new allotment.  Although not all responded, the response rate was pretty good – 67%.  Note:  The 30 dollars is for food. Gas is a different amount given to the employees -  please do not assume the 30 dollars includes fuel.

January 2022 Master mf.xlsx  

You have a sample of 52 employees at ABC Enterprises, and this is a sample of the population.  We want to use this sample to learn about the entire population of workers at the company.  We are going to treat the population as if it is not a finite population.

Annie is a company employee who grew up with 7 older brothers.  She noticed that they tended to eat more than she did, and she assumed that this characteristic applied to the general population.  In other words, she believes that males eat more than females.  She wondered if the proportion of male employees in the company was impacting the survey results.

Answer these questions:

. What proportion of the sample are male? 

. Why can't we say that the proportion of male employees in the entire country is the same as the proportion of male employees in the sample? 

. Section 9.4 discussed the Confidence Intervals for a population proportion. We are going to determine a 95% confidence interval for the proportion of employees in the entire company that are male. What is the z sub alpha over two value for a 95% confidence interval? What is the value of n? 

. Use the formula to create the confidence interval for the proportion of male employees in the entire company. Remember order of operations (you should be starting by working what is under the square root sign). What is your confidence interval? 

· Why is there a range for the answer instead of one single value like there was in your first response in this post? 

· Calculate the 99% confidence interval for the proportion of the population who are male. 

· Compare the range of the 95% confidence interval to the range of the 99% confidence interval. What happened, and why? 

· How would you respond to Annie's concern about the proportion of males in the company affecting the dollar amount?