Final Exam (Written Portion) - 1100Q Spring 2021
***Please make sure you also complete the multiple-choice portion in
Please round all decimals to 2 points to the right of the decimal. Relax and do
your best. That’s all you can ever ask from yourself in life.
1. Sampling Distributions
Suggested Time: 16 minutes
a. (3 points) Visually depict what the sampling distribution of sample
population of Sample proportion
Nne25 As a
Apn 5125 In 25 adataset
for I425 Pwe can
collect the acenterspread
Sn paes p
b. The estimated percent of people in the world that prefer Friends over
Seinfeld is .07. Austin suspects that this is a bit high. To check his claim, he
collects a simple random sample of 200 people, of which 12 say they
prefer Friends over Seinfeld.
i. (2 points) Write down the given information. Be sure to use
the appropriate parameter and/or statistic notation.
ii. (3 points) Describe the shape, center, and spread of the
sampling distribution of 𝒑
̂ (hint: √.𝟎𝟎𝟎𝟑𝟐𝟓𝟓 =. 𝟎𝟐).
iii. (3 points) Draw this distribution, labeling the mean, each
standard deviation mark as we did in class, and the
n200 Sample size n200
p0.07 sample proportionlpnt sus.cc z2oo 0.06
15 0006 population proportionLp 0.07
10 200 0.07 14 Shape nip 10 nu p10 nis random
14310 ph is approximatelynormal
110 20011 0.07 spread µop p0.07
2001093 sampling distribution t.p JPLT
n.JO 093 o.o
186 10 200
0.01 0.03 0.05 0.07 0.09 OIl 0.13
iv. (3 points) Is the observed statistic a reasonable value to get
given the assumed population proportion p = .07? Support
your answer with a calculated z-score.
2. Hypothesis Testing – One Sample
Suggested Time: 18 minutes
a. (2 points) What is the main goal of inference?
b. The average number of students at each university with gym
memberships outside of their respective university’s fitness center was
1231 in 2017. In an effort to study whether this trend is increasing in 2018
and thus UConn’s investment in a new student fitness center is
unnecessary, UConn researchers took a simple random sample of 34
universities. They found that the average number of students with
external gym memberships from the 34 universities was 1233 with a
standard deviation of 11.
i. (2 point) Use point estimation to estimate the average
number of students at each university with gym
memberships outside of their respective university’s fitness
center. How does this compare with the known mean?
PffO06 PZEO06 O07 PZCOs
PlZfO5a0.3085 from 2table
pFEO06 0.3085 O05
Therefore it is reasonable
can't conclude that population proportion is less than 0.07
Parameters are usually unknown population is too large so we
calculate statistics from properly conducted samples to estimate
XNMr2 then ECx eee
ELIK EEti In EElxil nntt.ie
Iis unbiased estimator for ie
Point estimate of avg no of students at each
university with gym memberships outside of
their University's fitness center is 1233