Question

In: Statistics and Probability

. Twin Peaks Lingerie, Incorporated, wants to introduce a new bustier, to be marketed under the...

. Twin Peaks Lingerie, Incorporated, wants to introduce a new bustier, to be marketed under the Lady Gagatm 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?

Solutions

Expert Solution

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.


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