6.6
(a) False. A confidence interval is constructed to estimate the population 
proportion, not the sample proportion.

(b) True. 95% CI: 46% ± 3%.

(c) True. By the definition of the confidence level.

(d) False. As confidence goes down, margin of error goes down as well.

6.12
(a) Sample statistic. Since it represents response from the survey takers only.

(b) 

SE <- sqrt(.48*(1 - .48)/1259)
lo <- .48 - 1.96 * SE
hi <- .48 + 1.96 * SE
c(lo, hi)

## [1] 0.4524028 0.5075972

We are 95% confident that 45.24% to 50.75% of US residents approve legalizing
marijuana

(c) This is a random sample from less than 10% of the population, so the 
observations are independent. 
Success-failure condition is satisfied:

(success <- .48 * 1259)

## [1] 604.32

(failure <- (1 - .48) * 1259)

## [1] 654.68

both well above 10.

(d) Since the 95% confidence interval barely covers 50%, the news piece's
statement is not justified.

6.20

n <- 1.96^2 * 0.48 * 0.52 / 0.02^2
ceiling(n)

## [1] 2398

6.28

p_ca <- 8/100
p_or <- 8.8/100
n_ca <- 11545
n_or <- 4691

se <- sqrt(p_ca * (1 - p_ca) / n_ca + p_or * (1 - p_or) / n_or)
point_est <- p_ca - p_or
lo <- point_est - 1.96 * se
hi <- point_est + 1.96 * se
c(lo, hi)

## [1] -0.017498128  0.001498128

We are 95% confident thatat the true proportion of Californians having sleep
deprivation is 1.75% lower to 0.15% higher than Oregonians having sleep
deprivation.

6.44
(a) H0: Barking deer prefer each habitat equally likely
    HA: Barking deer prefer some habitat over other
    
(b) Use a chi-squared goodness of fit test.

(c)           Woods  Cultivated grassplot Deciduous forests Other    Total
    Acutal      4              16                  61       345       426  
    Expected   20.448        62.622               168.696   174.234   426

    Independence: As it is not provided if sample is random, we have to assume 
    it.
    Sample size: All expected counts are atleast 5 
(d)

chi_sq <- (4 - 20.448)^2/20.448 + (16 - 62.622)^2/62.622 + 
  (61 - 168.696)^2/168.696 + (345 - 174.234)^2/174.234
chi_sq

## [1] 284.0609

df <- 3

Since the p-value is less than 5%, we reject H0.
There is convincing evidence that barking deers prefer certain habitats over
others.

6.48
(a) Use a chi-squared goodness of fit test.

(b) H0: There is assosciation between caffeinated coffee consumption and
        risk of depression in women. 
    HA: There is no assosciation between caffeinated coffee consumption and
        risk of depression in women.
    
        
(c)         

48132 / 50739

## [1] 0.9486194

(d) 

(expected <- (2607 / 50739) * 6617)

## [1] 339.9854

observed <- 373
(observed - expected) ^ 2 / expected

## [1] 3.205914

(e)
df = 4
p < 0.001

(f)
Since the p-value is less than 5%, we reject H0. There is no convincing evidence 
to show assosciation between coffee intake and depression.

(e) 
I agree with it. Since this is an observational study, we cannot make 
conclusions based on it.