Question

TRY IT 1.11 You are going to use the random number generator to generate different types of samples from the data. This table displays six sets of quiz scores (each quiz counts 10 points for an elementary statistics class #1 #2 #3 34 #5 #6 5 7 10 9 8 10 5 9 8 7 6 9 10 8 6 7 9 9 10 10 9 8 9 7 8 9 5 7 4 9 9 9 10 8 7 7 7 10 9 8 8 8 9 10 8 8 9 7 8 7 7 8 8 8 10 9 B 7 Table 1.6 Instructions: Use the Random Number Generator to pick samples. 1. Create a stratified sample by column. Pick three quiz scores randomly from each column. o Number each row one through ten On your calculator, press Math and arrow over to PRB. For column 1, Press 5crandint and enter 1,10). Press ENTER. Record the number. Press ENTER 2 more times (even the repeats). Record these numbers. Record the three quiz scores in column one that correspond to these three numbers. Repeat for columns two through six. These 18 quiz scores are a stratified sample. 2. Create a cluster sample by picking two of the columns. Use the column numbers: one through six. o Press MATH and arrow over to PRB.

Answer 1

1.To create a stratified sample by column, we pick three quiz scores randomly from each column.

Hence the stratified sample of 18 quiz scores will be,

9, 8, 9, 10 ,8, 5, 10, 9, 9, 5, 7, 9, 8, 7, 8, 6, 7,4

2. To create a cluster sample by picking two of the columns randomly where column numbers are one through six.

Hence the cluster sample will be,

1^st Cluster : 9, 8, 10, 7, 6, 9

2nd Cluster: 8, 7, 4, 6, 9, 8

3. 50 random number values between zero and one are as follows:

0.2137   0.3283   0.9776   0.1169   0.7169  

0.9735   0.5649   0.7303   0.7479   0.2456  

0.3178   0.3706   0.0514   0.5176   0.0966  

0.9723   0.5052   0.2766   0.7451   0.9467  

0.8997   0.5548   0.2549   0.2384   0.7572  

0.1278   0.5277 0.6288   0.3661   0.0882  

0.0921   0.2176   0.3452   0.0566   0.7557  

0.7362   0.5896   0.0146   0.5970   0.1210  

0.9752   0.7363   0.1712   0.9229   0.7144  

0.8123   0.1705   0.1743   0.5650   0.9636

   

4. Descriptive statistics for above random numbers,

• Sample mean :

  

N X X į = 1 N

= 0.4918

• Sample Standard deviation:

S = (x - x) N - 1

= 0.3102

• First quartile:

    

Q1 = xy + z(xy + 1 - Xy)

= 0.2147   

y	truncated integer value of w
w	N + 1 4
z	fraction component of w that was truncated
xj	jth observation in the list of sample data, ordered from smallest to largest

• Third quartile:

  

Q3 = xy + z(xy + 1 - Xy)

= 0.7429

y	truncated value of w
w	3(N + 1) 4
z	fraction component of w that was truncated away
xj	jth observation in the list of sample data, ordered from smallest to largest

• Median:

Median = the middle value of a set of ordered data.

= 0.5227