Kapitel 11 &12

Axel Duvebäck & David Sivén

require(mosaic)

11.01

a) TRUE

b) TRUE

a) Quantile, 65

qnorm(0.01, mean = 100, sd = 15)
## [1] 65.1

b) Quantile

c) Left end of interval: 90

Right end of interval: 110

qnorm(c(0.25, 0.75), mean = 100, sd = 15)
[1]  89.88 110.12

d) Left end of interval: 81

Right end of interval: 119

qnorm(c(0.1, 0.9), mean = 100, sd = 15)
[1]  80.78 119.22

e) 0.41

pnorm(120, mean = 100, sd = 15)
[1] 0.9088
pnorm(100, mean = 100, sd = 15)
[1] 0.5
0.9087888 - 0.5
[1] 0.4088

11.05

a) Min & Max

b) Mean & Standard Deviation

c) Average Number per Interval

d) Average Number per Interval

e) Probability and Size

11.10

a) Binomial

b) Normal

c) Binomial

11.23

a) It is binomial.

b) It's not for both of the above reasons.

c) It's not because the probability is not fixed for every individual component. (Eftersom vi inte vet storleken på meningarna.)

d) It is binomial.

e) It is binomial.

f) It's not because the sample size is not fixed.

g) It is binomial. Beroende på hur lotteriet är utformat.

12.01

a) point.estimate

b) margin.of.error

c) confidence.level

12.02

a) C

b) B

12.04

B

12.10

1. Point estimate: 9.19 Margin of error: 0.211

feet = fetchData("kidsfeet.csv")
Retrieving from http://www.mosaic-web.org/go/datasets/kidsfeet.csv
mean(width ~ sex, data = feet)
    B     G 
9.190 8.784 
summary(lm(width ~ sex, data = feet))

Call:
lm(formula = width ~ sex, data = feet)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.8842 -0.2900  0.0158  0.4600  0.7158 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    9.190      0.106   86.97   <2e-16 ***
sexG          -0.406      0.151   -2.68    0.011 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.473 on 37 degrees of freedom
Multiple R-squared:  0.163, Adjusted R-squared:  0.14 
F-statistic: 7.18 on 1 and 37 DF,  p-value: 0.0109
0.1057 * 2
[1] 0.2114

2. Point estimate: 8.99 Margin of error: 0.16

mean(width, data = feet)
[1] 8.992
summary(lm(width ~ 1, data = feet))

Call:
lm(formula = width ~ 1, data = feet)

Residuals:
    Min      1Q  Median      3Q     Max 
-1.0923 -0.3423  0.0077  0.3577  0.8077 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)   8.9923     0.0816     110   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.51 on 38 degrees of freedom
0.0816 * 2
[1] 0.1632

3. Point estimate: 0.406 Margin of error: 0.30

summary(lm(width ~ sex, data = feet))

Call:
lm(formula = width ~ sex, data = feet)

Residuals:
    Min      1Q  Median      3Q     Max 
-0.8842 -0.2900  0.0158  0.4600  0.7158 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)    9.190      0.106   86.97   <2e-16 ***
sexG          -0.406      0.151   -2.68    0.011 *  
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 0.473 on 37 degrees of freedom
Multiple R-squared:  0.163, Adjusted R-squared:  0.14 
F-statistic: 7.18 on 1 and 37 DF,  p-value: 0.0109
0.1514 * 2
[1] 0.3028