Page 63: 1.50, 1.52, 1.54

Exercise 1.50

  1. It appears that though most of the patients died, a much larger percentage of the treatment group survived than the control group. So no, survival is not independent of whether or not the patient got a transplant.

  2. The box plot shows the dramatic difference in survival time for those who got the treatment vs. the control group, but it does show that there was one outlier case in the control group who also had a long survival time.

Exercise 1.52

  1. 88% of the control group died, and 65% of the treatment group died.

    1. Claims: a heart transplant makes longer survival more likely. A heart transplant does not make a difference in a longer life for heart patients.
    1. 51, 52. 69, 34. 0. 23%.
Exercise 1.54

  1. Experiment because it selects a group of people to prove or disprove a hypothesis

  2. Yes, the study makes use of blinding the subjects by giving some the drug and some a placebo.

  3. At first glance it does not appear that the antibiotic or the placebo is more or less effective on sinusitis, because the difference is only 2%.

  4. The independence model would be that use of an antibiotic is no more effective on sinusitis than use of a placebo, so antibiotics would not be indicated for sinusitis. The alternative model would be that a 10 day course of antibiotics is an effective treatment for sinusitis.

  5. The evidence does not favor the alternative model.

Page 107: 2.1(a), 2.3, 2.5

Exercise 2.1 a

False. We don’t have all the information about how many rolls in total or anything like that.

Exercise 2.3

  1. 10 tosses

  2. 100 tosses

  3. 100 tosses

  4. 10 tosses

Exercise 2.5

  1. .5^10

  2. .5^10

  3. 1-(.5^10) = 1-.001 = .999

Lab 2

Exercise 3.1
pnorm(-1.35,0,1)
## [1] 0.08850799
1-pnorm(1.48,0,1)
## [1] 0.06943662
pnorm(1.5,0,1)-pnorm(0.4,0,1)
## [1] 0.2777711
pnorm(2,0,1)-pnorm(-2,0,1)
## [1] 0.9544997

d.|Z|>2, -2>z>2

pnorm(-2,0,1)-pnorm(2,0,1)  
## [1] -0.9544997
Exercise 3.2

What percent of a standard normal distribution is found in each region? N(0,1)
a. Z>-1.13

1-pnorm(-1.13,0,1)  
## [1] 0.8707619
  1. Z<0.18
pnorm(0.18,0,1)  
## [1] 0.5714237
  1. Z>8
1-pnorm(8,0,1)  
## [1] 6.661338e-16

d.|Z|<0.5, -.05 N(462,119), QR-> N(584,151)

(620-462)/119
## [1] 1.327731
(670-584)/151
## [1] 0.5695364

For verbal reasoning, her Z score was 1.328, and for the quantitative reasoning, her Z score was 0.570.

  1. They give the number of standard deviations above the mean.

  2. She did better on the verbal reasoning part of the exam.

pnorm(620,462,119)
## [1] 0.9078665

She was in the 91st percentile for the verbal reasoning.

pnorm(670,584,151)
## [1] 0.7155039

She was in the 72nd percentile for the quantitative reasoning.

1-pnorm(620,462,119)
## [1] 0.09213348
1-pnorm(670,584,151)
## [1] 0.2844961

There were 9% above her in verbal reasoning, and 28% above her in quantitative reasoning.

  1. We need to use the Z score to see how well she did relative to her peers. Her raw scores don’t show that.
Exercise 3.4

  1. M30-34-> N(4313,583) W25-29-> N(5261,807)

(4948-4313)/583
## [1] 1.089194
(5513-5261)/807
## [1] 0.3122677

Leo’s Z score is 1.09, and Mary’s is .312. This tells me that Leo’s time relative to the other men in his age group was faster than Mary’s time relative to the other women in her age group, so Leo did better. Jerk.

  1. Leo did better in his respective group because he did 1.09 standard deviations above the mean, while Mary only did .312 better than the mean.

pnorm(4948,4313,583)
## [1] 0.8619658

Leo finished faster than 86% of his group.

pnorm(5513,5261,807)
## [1] 0.6225814

Mary finished faster than 62 percent of her group.

  1. If the distributions of finishing times are not normal, that would change the mean, so it would definitely change those calculations.
Exercise 3.5
qnorm(.8,584,151)
## [1] 711.0848

In order to be in the 80th percentile, you have to score better than 711.

qnorm(.3,462,119)
## [1] 399.5963

He scored about 400 on the Verbal Reasoning part of the GRE.

Exercise 3.6
qnorm(0.95,4313,583)
## [1] 5271.95

The cutoff time for the fastest 5% athletes in the men’s group is 5271.95 seconds.

qnorm(.1,5261,807)
## [1] 4226.788

The cutoff time for the slowest 10% of athletes in the women’s group is 4226.8 seconds.

Exercise 3.10
pnorm(48,55,6)
## [1] 0.1216725

A randomly chosen 10 year old has a 12% chance of being shorter than 48 inches.

pnorm(65,55,6)-pnorm(60,55,6)
## [1] 0.154538

There is a 15% chance that a randomly chosen 10 year old will be between 60 and 65 inches.

qnorm(.9,55,6)
## [1] 62.68931

A 10 year old 62.7 inches or above would be considered very tall.

pnorm(54,55,6)
## [1] 0.4338162

Around 43% of 10 year olds cannot go on the batman ride.

Exercise 3.12
pnorm(80,72.6,4.78)
## [1] 0.939203

94% of drivers go slower than 80 miles/hour.

pnorm(80,72.6,4.78)-pnorm(60,72.6,4.78)
## [1] 0.9350083

About 93% of drivers go between 60-80 miles/hour.

qnorm(.95,72.6,4.78)
## [1] 80.4624

The fastest 5% drive about 80.46 miles/hour.

1-pnorm(70,72.6,4.78)
## [1] 0.7067562

Around 71% of drivers on the I5 are driving faster than the speed limit.

Exercise 3.13
1-pnorm(50,45,3.2)
## [1] 0.05908512

About 6% of passengers will incur this fee.

Exercise 3.18
fh=c(54,55,56,56,57,58,58,59,60,60,60,61,61,62,62,63,63,63,64,65,65,67,67,69,73)

I couldn’t do 3.17 because I couldn’t find the code you were talking about in the video, and I tried really hard to just type it in from the lab video, but it did not work.

Exercise 3.19

Yes, bar graph looks like a bell curve and is unimodal and symmetrical, and the dots on the plot are linear.