Exercise 7.1

1.

To set ideas, obtain a 95% confidence interval for $\mu$ if the data are:

       10   12  16  18  24

Do this one by hand. The sample mean and standard deviation are easy to get and $\sqrt{5} = 2.24$.

2.

Obtain a 95% confidence interval for $\mu$ if the data are:

      76  87  98 102 111 114 115 115 120 126

First boxplot the data. Next mark the sample average and the endpoints of the confidence interval on the plot. Here's some output from the summary module to do the confidence interval:

Rweb:> summary(variables)  
        x         
 Min.   : 76.0   
 1st Qu.: 99.0   
 Median :112.5   
 Mean   :106.4   
 3rd Qu.:115.0   
 Max.   :126.0   

Rweb:> var(variables)  
         x 
x 242.9333

3.

Obtain a 95% confidence interval for $\mu$ if the data are:

      6   8  14  30  31  32  51  57  87  87 109 145 156 171 342

First boxplot the data. Next mark the sample average and the endpoints of the confidence interval on the plot. Here's the output from the summary module to do the confidence interval:

Rweb:> summary(variables)  
        x         
 Min.   :  6.0   
 1st Qu.: 30.5   
 Median : 57.0   
 Mean   : 88.4   
 3rd Qu.:127.0   
 Max.   :342.0

Rweb:> var(variables)  
         x 
x 7885.543

4.

Consider the following sample of Etruscan skull sizes: Obtain a 95% confidence interval for $\mu$.

      141    145    145    146    142    126    144    146    154    149    143 131

(Ans: $142.6 \pm 4.25$).

5.

Same as the last question for a sample of size 10 of Italian skull sizes:

       134    132    126    134    131    130    130    125    132    126

(Ans: $130 \pm 2.04$).

6.

Plot the confidence intervals from the last two problems on a line. What do conclude about the true mean skull sizes of Etruscans and Italians based on this comparison?

7.

Now use all the Etruscan and Italian data to do the last three exercises. The data can be found by clicking HERE .

2000-08-26