In: Math
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)
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