STAT 200 Quiz 3 Section 6380

A quiz covering key statistical concepts for STAT 200 students.

Christopher Lee
Contributor
4.3
55
about 1 month ago
Preview (2 of 5)
Sign in to access the full document!
1
STAT 200 QUIZ 3 Section 6380 Summer 2015
(For Questions 1 & 2) Mimi was the 5th seed in 2014 UMUC Tennis Open that took place in
August. In this tournament, she won 80 of her 100 serving games. Based on UMUC Sports
Network, she wins 75% of the serving games in her 5-year tennis career.
1. (2 pts) Find a 90% confidence interval estimate of the proportion of serving games Mimi
won. (Show work and round the answer to three decimal places)
90% confidence interval estimate of the proportion of serving games Mimi won = (.8- 1.645*
sqrt(.75*.25/100 , .8+ 1.645* sqrt(.75*.25/100 ) = (.729, .871)
2. (5 pts) In order to determine if this tournament result is better than her career record of 75%.
We would like to perform the following hypothesis test:
𝐻0: 𝑝 = 0.75
𝐻: 𝑝 > 0.75
(a) (2 pts) Find the test statistic. (Show work and round the answer to two decimal places)
z= (.8-.75)/sqrt(.75*.25/100) = .05/.0433 = 1.15
(b) (2 pts) Determine the P-value for this test. (Show work and round the answer to three
decimal places)
P(z> 1.15)= 1- P(z<1.15)= 1- .875 = .125
(c) (1 pt) Is there sufficient evidence to justify the rejection of 0H at the α = 0.02 level?
Explain. There is insufficient evidence to justify the rejection of 0H at the α = 0.02 level as the
p-value of .125> α=.02.
3. (5 points) The SAT scores are normally distributed. A simple random sample of 225 SAT
scores has a sample mean of 1500 and a sample standard deviation of 300.
(a) (1 pt) What distribution will you use to determine the critical value? Why?
z ~N(0,1)
SAT scores are normally distributed and n=225
(b) (3 pts) Construct a 95% confidence interval estimate of the mean SAT score. (Show work
and round the answer to two decimal places)
95% confidence interval for 𝜇 : ( xbar 1.96*300/sqrt(225) , xbar + 1.96*300/sqrt(225))=(1500-
Preview Mode

Sign in to access the full document!

100%

Study Now!

XY-Copilot AI
Unlimited Access
Secure Payment
Instant Access
24/7 Support
Document Chat

Document Details

University
University of Maryland
Subject
Statistics

Related Documents

View all