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

a) As we are testing here whether the actual proportions of content differ from Essential Wear's claim, therefore the null and the alternative hypothesis here are given as:

H0: The actual proportions of content do not differ from Essential Wear's claim

Ha: The actual proportions of content differ from Essential Wear's claim

The alternative hypothesis is the claim here as given in the problem.

b) There are 5 categories here. For k - 1 = 4 degrees of freedom and 0.05 level of significance, this is a one tailed test and therefore we have from chi square distribution tables here:

$P(\chi^2_4 > 9.4877) = 0.05$

Therefore 9.4877 is the critical value here. This is given in graph here as:

0.20 0.15 0.10 0.05 0.00 0 2 4 6 10 12 14 8