Stat141  10/25
Inference for a single mean (including paired data and proportions) SW text Ch.6,9.

> civec =c(.9, .95, .99)
> errvec = 1 - civec     #alpha = 1 - confidence (prob of coverage)
> errvec
[1] 0.10 0.05 0.01
> qnorm(1 - errvec/2)
[1] 1.644854 1.959964 2.575829
> qt(1 - errvec/2,5)
[1] 2.015048 2.570582 4.032143
> qt(1 - errvec/2,25)
[1] 1.708141 2.059539 2.787436
> qt(1 - errvec/2,50)
[1] 1.675905 2.008559 2.677793

> #cockroach respiration (9/27)
> croach = c(55.95, 68.24, 52.73, 21.5, 23.78)
> mean(croach)
[1] 44.44
> sd(croach)
[1] 20.7408
> mean(croach) - 1.96*sd(croach)/sqrt(5); mean(croach) + 1.96*sd(croach)/sqrt(5)
[1] 26.25989
[1] 62.62011
> #endpoints of 95% CI if one assumes 5-1 is "very large"

> mean(croach)-qt(.975,4)*sd(croach)/sqrt(5);mean(croach)+qt(.975,4)*sd(croach)/sqrt(5)
[1] 18.68689
[1] 70.1931
> qnorm(.975);qt(.975,4)
[1] 1.959964
[1] 2.776445

> t.test(croach)                            > t.test(croach, c= .9)                
        One Sample t-test                           One Sample t-test               
data:  croach                               data:  croach                          
t = 4.7911, df = 4, p-value = 0.008705      t = 4.7911, df = 4, p-value = 0.008705 
alternative hypothesis: true mean           alternative hypothesis: true mean      
  is not equal to 0                            is not equal to 0                   
95 percent confidence interval:             90 percent confidence interval:        
 18.68689 70.19311                           24.66591 64.21409                     
sample estimates:                           sample estimates:                      
mean of x                                   mean of x                              
    44.44                                       44.44                              

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> #paired data SW Ch.9 is single mean inference, mean of differences     
> #SW ex 9.6 p.354 squirrels (SW already computed diff)
> sqr = read.table(file="D:\\stat141\\squirrel.dat", header = T)
> summary(sqr)
     person           tree         difference     
 Min.   : 60.0   Min.   : 34.0   Min.   :-217.00  
 1st Qu.:126.5   1st Qu.: 47.5   1st Qu.: -11.50  
 Median :189.0   Median : 54.0   Median : 144.00  
 Mean   :190.2   Mean   :118.3   Mean   :  71.91  
 3rd Qu.:239.0   3rd Qu.:186.5   3rd Qu.: 167.50  
 Max.   :326.0   Max.   :293.0   Max.   : 275.00  
> sqr
   person tree difference                  person tree difference                            
1      81  137        -56               7     240   45        195  
2     178   34        144               8     326  293         33  
3     202   51        151               9      60  277       -217  
4     325   50        275               10    119   83         36  
5     238   54        184               11    189   41        148  
6     134  236       -102
> attach(sqr)
> #note SW normal prob plots (qq-plot via qnorm) to check distrib assumptions
> t.test(difference);t.test(difference, c=.9)
        One Sample t-test                           One Sample t-test              
data:  difference                           data:  difference                      
t = 1.6113, df = 10, p-value = 0.1382       t = 1.6113, df = 10, p-value = 0.1382  
alternative hypothesis: true mean           alternative hypothesis: true mean      
       is not equal to 0                         is not equal to 0                 
95 percent confidence interval:             90 percent confidence interval:        
 -27.52795 171.34613                          -8.977145 152.795327                 
sample estimates:                           sample estimates:                      
mean of x                                   mean of x                              
 71.90909                                    71.90909                              
> qt(1 - errvec/2,10)
[1] 1.812461 2.228139 3.169273
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