Share
Explore BrainMass

Inference about Population Proportion

Part I:  In this exericse, we have a box of paint cans for a project kit.  The box contains 100 bottles
in total, with the following colors:   yellow,  black,  green,  blue.
 
We will randomly select 15 bottles from the box and count how many are yellow.   
 
Try the sampling 10 times.  You should get some range on the number of yellow cans and an average proportion.
Record This Information! (If you take more than 10 samples, the Mean Proportion is based on the last 10 samples.)

No. of Yellow: 5 6 7 5 6 7 4 5 5 7
Mean Proportion > 0.38
Part II:  We assume that our 10 samples provide a reasonable guess for the population proportion P to use in the
following calculations, that is, we will set phat to the Mean Proportion calculated above.
 
  You will test one or more values of P0 based on the equation >>      z =
              

 
Enter your P0 value then test for below:

 Enter your P0 value >

 z-statistic    probability    80% Confidence Int.   90% Confidence Int.

Inference about Population Proportion
 
     >>  Two-Sample Proportions and Confidence Interval
 
 In this exericse, we have two boxes of paint cans, each box containing 100 bottles in total.  

 Define the population proportion of Box 1 as p1, and that of Box 2 as p2.
 We will take simple random samples from each box, determine the sample proportions.  We wish
 to determine if the population proportions are equal.
 
 Box 1 sample proportion is pHat1 = Box 1 sample # yellow ÷ Sample size (=n1)
 Box 2 sample proportion is pHat2 = Box 2 sample # yellow ÷ Sample size (=n2)
                                               pHat = # yellow in both samples ÷ (n1+n2)   
 
 z =
n1=17 n2=20

Box 1 Box 2 < Sample From 
8 6 < No. of Yellow 
17 20 < No. in Sample
0.471 0.3 < pHat Value 
0.171 < pHat1 - pHat2
1.066 < Z value
(-0.039, 0.350) < 80% Conf.Interval

Answer the following:

State Hypothesis Ho >
State Hypothesis Ha >
 Enter Conclusion Statement >

Attachments

Solution Summary

Excel file attached answers multiple part questions on random sampling paint boxes and two-sample populations with confidence intervals.

$2.19