Question

1. The researcher also has been asked to determine at both the 5% and 2% levels of significance whether the proportion stores that experiences at least a 20% return rate for the shirt within 90 days of purchase is different from 15%. She selects a random sample of stores from the population of stores she is studying. The sample data concerning whether the store experiences a rate of return of at least 20% is shown in appendix two below. Answer the question concerning whether the proportion of stores that experiences a rate of return of at least 20% differs from 15%. If you arrive at different results for the two parts of this problem, provide a reason for that difference.

Appendix Two: (Store experiences a rate of return of at least 20%? Y = yes, N = no)

            N         Y         Y         N         N         N         N         N         N         N         N

            Y         N         N         N         N         Y         N         Y         N         N         Y

            Y         N         N         N         N         N         N         N         N         Y         N

            N         N         N         Y         Y         N         N         N         N         N         N

            N         Y         Y         Y         N         N         N         Y         N         N         N

            Y         N         Y         N         N         N         N         N         N         N         Y

Answer 1

Total no of stores 66

Stores with Yes = 17 therefore with no will be 49

Let %

We are asked to check at 5% and 2% whether proportion differs from 15%

where = 15%

Test Statistic (T.S.)= =

T.S. =1.9985

Decision criteria : Reject if T.S. >

Critical region (We will use 2-tailed normal dist )

1)

at 5%

=1.96

Since 1.9985>1.96 therefore T.S.>   

Conclusion: We reject at 5% level of significance and conclude that proportion of stores with at least 20% rate of return are is not 15%.

2)

at 2%

=2.1701

Since 1.9985<2.1701 therefore T.S. <

Conclusion: We do not reject at 2% level of significance and conclude that proportion of stores with at least 20% rate of return are is 15%.

We get two different results due to different levels of significance. Hypotheses testing is done to check whether at a given level of significance the value of (for binomial) can be used as the population parameter or not. The level is also used to calculate the confidence intervals (range of values that the parameter can take). Lower the level stricter the test(strong evidence is required to reject null hypo) and so we might end up with not rejecting the null hypo. Vice versa with higher level.

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