STAT 200 Homework 4 Due Date: September 23, 2016

1. We often see players on the sidelines of a football game inhaling oxygen. Their coaches think this will speed their recovery. We might measure recovery from intense exercise as follows: Have a football player run 100 yards three times in quick succession. Then allow three minutes to rest before running 100 yards again. Time the final run. Because players vary greatly in speed, you plan a matched pairs experiment using 30 football players as subjects.

a. Describe the design of such an experiment to investigate the effect of inhaling oxygen during the rest period.

b. Why should each players two trials be on different days?

c. Use Table B at line 135 or Rs sample function to decide which players will get oxygen on their first trial.

2. A club has 30 student members and 10 faculty members. The students are

Abel

Fisher

Huber

Moran

Reinmann

Carson

Golomb

Jimenez

Moskowitz

Santos

Chen

Griswold

Jones

Neyman

Shaw

David

Hein

Kiefer

OBrien

Thompson

Deming

Hernandez

Klotz

Pearl

Utts

Elashoff

Holland

Liu

Potter

Vlasic

And the faculty members are

Andrews

Fernandez

Kim

Moore

Rabinowitz

Besicovitch

Gupta

Lightman

Phillips

Yang

The club can send 6 students and 2 faculty members to a convention and decides to choose those who will go by random selection. Using a stratified random sample of 6 students and 2 faculty members, display who you chose and explain how you got that sample.

3. The figure shows histograms of 4 sampling distributions of statistics intended to estimate the same parameter (the red dashed line). Label each distribution relative to the others as having high or low bias and as high or low variability.

4. What are the popular ringtones? The website funtnoia.com updates its list of top ringtones frequently. Here are probabilities for the top 10 ringtones recently listed by the site:

Ringtone

Probability

Carmina Burana Trans-Siberian Orchestra

0.328

Halo Beyonc

0.123

7 Years Lukas Graham

0.103

Stressed Out Twenty One Pilots

0.089

Dont Let Me Down The Chainsmokers

0.068

I Took A Pill In Ibiza Mike Posner

0.062

Unsteady X Ambassadors

0.062

Work From Home Fifth Harmony

0.055

Cheap Thrills Sia

0.055

All Or Nothing Elliphant

0.055

a. What is the probability that a randomly selected ringtone from this list is either Dont Let Me Down or I Took A Pill In Ibiza?

b. What is the probability that a randomly selected ringtone from this list is not Dont Let Me Down and not I Took A Pill In Ibiza?

c. If two ringtones are selected independently, what is the probability that both are Halo?

d. Describe in words the complement of the event in part c. Find the probability of this event.

5. All human blood can be ABO-typed as one of O, A, B, or AB, but the distribution of the type varies a bit among groups of people. Here is the distribution of blood types for a randomly chosen person in the United States.

Blood type

A

B

AB

O

U.S. probability

0.42

0.11

0.03

?

a. What is the probability of type O blood in the United States?

b. Maria has type B blood. She can safely receive blood transfusions from people with blood types O and B. What is the probability that a randomly chosen person from the United States can donate blood to Maria?

c. Now suppose that the distribution of blood types in Ireland is below.

Blood type

A

B

AB

O

Ireland probability

0.35

0.10

0.03

0.52

Choose a person from the U.S. and a person from Ireland at random, independently of each other. What is the probability that both have type O blood?

d. Choose a person from the U.S. and a person from Ireland at random, independently of each other. What is the probability that both have the same blood type?