Question

11. 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.

Answer 1

Answer:-
Given that:-

a):distribution is same

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$H_{a}$distribution is different

b)level of significance ,$\alpha =0.01$

Degree of freedom =k-1=5-1=4

Critical value=13.277(Excel function =chisq.inv.rt($\alpha$,df)]

c)

observed frequency,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 ,$X^{2}=\sum (O_E)^{2}/E=10.454$

level of significance ,

g= 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 functiob:=chisq.inv.rt($\alpha$,df)]

d)Decesion:Pvalue >$\alpha$, Reject

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e)Proportion is different from claim.