In: Statistics and Probability
. 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?
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.
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