Question

. Twin Peaks Lingerie, Incorporated, wants to introduce a new bustier, to be marketed under the Lady Gaga^tm logo. They have tested four sizes of bustier, from tiny to “almost-not-there.” A sample of 200 teenaged boys each stated their preference, as indicated in the table below. Is there a preferred size at the 0.05 level?

Size (in order)	Number Preferring
Tiny	10
Teeny-tiny	26
Teeny-weeny-tiny	64
Almost not there	100

State Hypotheses:

Show work:

What is the value of the test statistic?

What is the value of the standard?

What is the result of the test?

Answer 1

Ho: Order Size is independent(no prefered)  
H1:Order Size is not independent(prefered)  

observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
10	0.250	50.00			32.000
26	0.250	50.00			11.520
64	0.250	50.00			3.920
100	0.250	50.00			50.000

chi square test statistic,X² = Σ(O-E)²/E =   97.440              
                  
level of significance, α=   0.05              
Degree of freedom=k-1=   4   -   1   =   3
                  
       
                  
                  
Critical value =    7.8147   [ Excel function: =chisq.inv.rt(α,df) ]        

P value =   0.0000   [ excel function: =chisq.dist.rt(test-stat,df) ]          
Decision: P value < α, Reject Ho          

Hence there is a preferred size at the 0.05 level.

Please revert back in case of any doubt.

Please upvote. Thanks in advance.