Austin Menger

STAT 1100Q

1

Final Exam (Written Portion) - 1100Q Spring 2021

***Please make sure you also complete the multiple-choice portion in

HuskyCT. ***

Name:

ID Number:

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

Points: 14

a. (3 points) Visually depict what the sampling distribution of sample

proportions is.

Dhrasti Patel

2566809

Sample Distribution

population of Sample proportion

Nne25 As a

Apn 5125 In 25 adataset

for I425 Pwe can

sdescribe its

collect the acenterspread

Sn paes p

zshape

I

Sz pm

n25

1425

Austin Menger

STAT 1100Q

2

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

observed statistic.

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

TB0.02

0.01 0.03 0.05 0.07 0.09 OIl 0.13

M

Austin Menger

STAT 1100Q

3

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

Points: 20

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

T.o.la I

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

the parameters

it 1231

Ie1233

n34

TIl

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

I1233