Question

The data set of Froot loops list data from 100 boxes, and 27% of them are red color.  the Florida candy company claims that the percentage of red color depot loops is equal to 24%. use 0.05 significance level to test that claim. show work of how you,
1) identify the claim.
2)give symbolic form that must be true when the original claim is false.
3) identify Null and alternative hypothesis. 4)select significance level.
5) identify the test statistic
6)find P values
7) make a decision
8)restate decision in nontechnical terms.

Answer 1

1)

Claim:   p =    0.24

2)

p ╪   0.24

3)

Ho :   p =    0.24
H1 :   p ╪   0.24

4)

Level of Significance,   α =    0.05

5)

Sample Size,   n =    100                  
                          
Sample Proportion ,    p̂ =    0.2700                  
                          
Standard Error ,    SE = √( p(1-p)/n ) =    0.0427                  
Z Test Statistic = ( p̂-p)/SE = (   0.2700   -   0.24   ) /   0.0427   =   0.7024
                          

6)

p-Value   =   0.4824   [excel formula =2*NORMSDIST(z)]  

7)

Decision:   p value>α ,do not reject null hypothesis       

8)

There is not enough evidence to reject the claim that percentage of red color depot loops is equal to 24% at 5% level of significance