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.

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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)

Answer:

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)

Answer:

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)

Answer:

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)

Answer:

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)

Answer:

6. In a state, 50,000 students graduated from four-year not for profit colleges in 2017. Out

of these 50,000 graduates, 20,000 graduated from private colleges, and 30,000 graduated

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

graduate carried at graduation. The results are as follows:

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)

Answer:

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

basketball and football.

• 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)

Answer:

2

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