Question

Essential Wear is a company that sends 5 items of apparel every 3 months. They specialize in women's clothes and the boxes consist of undergarments, accessories, and loungewear. The subscriber pays a flat fee but they do not know what they will be getting in each box. The company claims that 20% of the goods sent are underwear, and 10% are bras, 18% are socks, 36% are loungewear, and 16% are accessories. Suppose a suspicious customer tally's the totals for the last 3 years and finds that the company sent 18 pairs of underwear, 4 bras, 16 pairs of socks, 12 loungewear pieces and 10 accessories. Test the claim that the actual proportions of content differ from Essential Wear's claim. Use a 0.05 level of significance. a. Write the null and alternative hypotheses. Label the claim. b. Draw the graph and shade the critical area(s). Place the critical value(s) on the graph. c. Fill in the following: Critical Value(s) Test Statistic P Value d. Circle one: REJECT H. or FAIL TO REJECT H e. Statement of conclusion:

Answer 1

a)

Ho: distribution is same
Ha: distribution is different

b)

level of significance, α=   0.01              
Degree of freedom=k-1=   5   -   1   =   4

Critical value =    13.277   [ Excel function: =chisq.inv.rt(α,df) ]          

c)

observed frequencey, O	expected proportion	expected frequency,E	(O-E)		(O-E)²/E
18	0.200	12.00	6.00		3.000
4	0.100	6.00	-2.00		0.667
16	0.180	10.80	5.20		2.504
12	0.360	21.60	-9.60		4.267
10	0.160	9.60	0.40		0.017

chi square test statistic,X² = Σ(O-E)²/E =   10.454                          
                              
level of significance, α=   0.05   
Degree of freedom=k-1=   5   -   1   =   4          
                              
P value =   0.0334   [ excel function: =chisq.dist.rt(test-stat,df) ]                      
                           
                              
                              
Critical value =    13.277   [ Excel function: =chisq.inv.rt(α,df) ]      

d)

Decision: P value >α , Reject Ho  

e)

Proportion is different from claim

  

Please let me know in case of any doubt.

Thanks in advance!

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