Question

Writing Assignment #1 Instructions
The following assignment should be typed and printed or handwritten and turned in to the CA office in room​ 201 TMCB.​ If there is no one in the CA Office, you can slip your assignment through the slot in the door.
You must follow the instructions below or you will not receive credit.​ You can turn in the assignment up until 5:00 PM on the due date.
Important Notices: If you do not staple multiple pages, you may lose points. If you do not put your section number on the paper, you may lose points. As shown below, please fold your paper lengthwise and on the outside write (a) your name, (b) Stat 121, (c) your section number, and (d) the assignment number. (An example is available outside the CA Office.)
The situation is as follows:
Rent and other associated housing costs, such as utilities, are an important part of the estimated costs of attendance at college. A group of researchers at the BYU Off-Campus Housing department want to estimate the mean monthly rent that unmarried BYU students paid during Winter 2019. During March 2019, they randomly sampled 366 BYU students and found that on average, students paid $348 for rent with a standard deviation of $76. The plot of the sample data showed no extreme skewness or outliers.

Calculate a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019.
STATE
What is a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019?
PLAN
1. State the name of the appropriate estimation procedure. ​(2pts)
2. Describe the parameter of interest in the context of the problem. ​(2pts)
SOLVE
1. Name the conditions for the procedure. ​(2pts)
2. Explain how the above conditions are met. ​(2pts)
3. Write down the confidence level and the t* critical value. ​(2pts)
4. Calculate the margin of error for the interval to ​two decimal places​. ​Show your work. ​(2pts)
5. ​Calculate the confidence interval ​to two decimal places​ and state it ​in interval form​. ​(2pts)
CONCLUDE
Interpret your confidence interval in context. Do this by including these three parts in your conclusion ​(3 pts)​:
● Level of confidence​ (1pt)
● Parameter of interest in context ​(1 pt)
● The interval estimate ​(1 pt)
FURTHER ANALYSIS
1. How would selecting a 95% level of confidence change the size of the calculated confidence interval? (1pt). Explain or justify your answer by recalculating (1pt) .

2. At a 95% level of confidence, what sample size would be needed to estimate the parameter of interest to within a margin of error of ± $25? Use σ = $76. ​(2pts)
3. Suppose that a second random sample of unmarried BYU students was conducted during March 2019. Using this data, the confidence interval was calculated to be ​($342.67, $349.35)​. ​Rounded to two decimal places​, what is the margin of error for this confidence interval? Show your work. (1pt)

Answer 1

first four questions done. Other answers can be found from the detailed solution given below.

Calculate a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019.

What is a 98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019?
98% confidence interval estimate for the mean monthly rent of all unmarried BYU students in Winter 2019 is (338.7176, 357.2824)

State the name of the appropriate estimation procedure.
Find the confidence interval using t statistics.

Describe the parameter of interest in the context of the problem
mean monthly rent of all unmarried BYU students