Question

Offices are getting more casual. Companies relax their formal dress code for many reasons: they want to attract top candidates, to create a more relaxed work environment and to allow employees to be creative with their dress, which may translate to job creativity and productivity. Two large companies, Company A and Company B, are considering whether they should relax the dress code for their office workers as well. Independently, they randomly sampled their office employees to collect their opinions, and the resulting data are provided in the table below. We are interested if the proportion of all office workers in Company A who would like their company to relax the dress code is different from the proportion of all office workers in Company B who would like their company to relax the dress code, using a 10% significance level.

	“Would you like your company to relax the dress code?”
Group	Yes	No	Total
1 = Company A office workers	138	146	284
2 = Company B office workers	144	96	240

Recall the Steps for Testing Hypotheses:
1) State the appropriate hypotheses (the significance level has been selected to be 10%).
2) Check the necessary assumption(s) (you may assume that you have two independent random samples).
3) Perform the appropriate test (include all supporting computations for the test statistic and p-value, and the complete sketch of the p-value).
4) Give your statistical decision and provide a conclusion in context.

Answer 1

1)

Ho : p1 = p2

Ha : p1 p2

2)

number of success and failures in each groups are more than 5

assumptions are satisfied

3)

	x	n	p
1	138	284	0.48591549
2	144	240	0.60000000

TS

-2.61

p-value = 2 P(Z > |TS|)

= 0.0091

4)

since p-value = 0.0091 < alpha (0.10)

we reject the null hypothesis

we conclude that there is sufficient evidence that the proportion of all office workers in Company A who would like their company to relax the dress code is different from the proportion of all office workers in Company B who would like their company to relax the dress code,

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