# Expert Answer :Random Sample, Confidence Interval, Simplified Sam

Solved by verified expert:Attached word doc is the assignment and attached pdr doc are the class notes. Please answer all 7 questions showing work at how you got to the final answer.
assignment_4___7_questions___stats.docx

scannednotesfromlivesession8_2.pdf

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1. Suppose you have drawn a simple random sample of 625 students from University X and
recorded how much money each student spent on text books in 2017. For your sample,
sample mean (X bar) is \$550, and sample standard deviation (s) is \$240. Construct a 99%
confidence interval for µ. (Show work)
2. Suppose you have drawn a simple random sample of 300 students from University X. In
this sample, 75 students took AP statistics at high school. Let π denote the proportion of
University X students who took AP statistics in high school. Construct a 99% confidence
interval for π. (Show work)
3. Let µ denote the average dollar sales of Red Bull by a grocery store in New York State in
2017. You want to use a simple random sample to determine μ within ± 0.06 μ with 99%
confidence. You know that the sales of Red Bull by a store is roughly proportional to the
sales of Poland Springs bottled water by a store. You also know that in 2017, the average
sales of Poland Springs bottled water by a store was \$12,000, and the standard deviation
in the sales of Poland Spring bottled water by a store was \$9000. Compute the sample
size you need. (Show work)
4. Let π be the proportion of Syracuse University students that own Apple iPhones. Suppose
you want to use a simple random sample to determine π within ±.05 and with 99%
confidence. If you do not have any prior idea of π, determine the sample size you need.
(Show work)
5. There are 25,000 full time college students at a university. You want to use a simple
random sample to determine, within ±1000 and with 99% confidence, how many out of
these 25,000 students own Apple computers. If you have no prior idea of how many,
determine the sample size you need. (Show work)
6. In a state, 50,000 students graduated from four-year not for profit colleges in 2017. Out
from public colleges. You have selected a stratified sample from the population of 2017
graduates in this state with graduates from public and private colleges as the two strata.
For each graduate in your sample, you recorded how much student debt, if any, the
1
(1) Private college graduates: n1 = 225, X-bar-1 = 27,000, s1 = 9000
(2) Public college graduates: n2 = 100, X-bar-2 = 24,000, s2 = 6000
Let µ denote the average debt of a 2017 graduate in this state. (This average is the
average of the whole population of graduates, public and private combined.) Construct a
99% confidence interval for µ. (Show work)
7. A researcher conducted a mail survey of the students of University X to determine what
percentage of these students were interested in purchasing a combined season ticket for
• She mailed out questionnaires to a simple random sample of 600 students. 90 students
responded to the mail survey. 72 out of these 90 students were interested in purchasing
the combined ticket.
• The researcher then randomly selected 150 students out of the 510 students who did not
respond to the mail survey, and contacted them by telephone. All of these 150 students
cooperated. 48 out these 150 students were interested in purchasing the combined ticket.
Let π denote the proportion of students at University X who were interested in purchasing the
combined basketball and football season ticket. Construct a 99% confidence interval for π.
(Show work)
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