Question

Six months after settling the strike, H&H worker union sued the firm for reneging on its promise to increase employee salaries. The union hired an independent consulting firm that randomly selected four H&H Bagels stores in different locations and asked the employees about their salaries before and after the strike. The mean salaries of all employees in each store before and after the strike are shown in the table below:

nyc h&H bagels store location	mean hourly salary before the strike	mean hourly salary after the strike
Brooklyn	12.60	12.80
Queens	10.40	10.50
Bronx	10.00	10.30
Manhattan	15.20	15.60

If you were the independent consultant, would you conclude that H&H management fulfilled their promise to increase the employee salaries at a=0.01 significance level? Support this conclusion using five-step hypothesis testing procedure.

Answer 1

this is paired t-test

also this is right-tailed test as we want to know if mean has increased

t-Test: Paired Two Sample for Means
	mean hourly salary before the strike	mean hourly salary after the strike
Mean	12.05	12.3
Variance	5.716666667	6.126666667
Observations	4	4
Pearson Correlation	0.999191658
Hypothesized Mean Difference	0
df	3
t Stat	-3.872983346
P(T<=t) one-tail	0.015233146
t Critical one-tail	4.540702859
P(T<=t) two-tail	0.030466292
t Critical two-tail	5.84090931

p-value for one-tail = 0.015233146 > alpha(0.01)

hence we fail to reject the null hypothesis

we conclude that there is not sufficient evidence that H&H management fulfilled their promise to increase the employee salaries