Question

In a certain region, data has been collected on the number of critically ill due to a pandemic for 10 days before and after a lockdown came into place. Data before and after are as follows: before [60, 69, 81, 86, 56, 91, 70, 77, 73, 90], after [51, 48, 81, 80, 67, 71, 78, 63, 66, 68]. The researchers do NOT believe that the underlying distributions are normal and apply a suitable statistical test to see whether the lockdown was useful. What are the correct test value and decision at a confidence level of 95%?

Your answer:
	8.0, Reject
	8.0, Fail to reject
	37.0, Fail to reject
	5.0, Fail to reject
	5.0, Reject
	37.0, Reject

Answer 1

Here is the difference table

Before	After	Difference
60	51	9
69	48	21
81	81	0
86	80	6
56	67	-11
91	71	20
70	78	-8
77	63	14
73	66	7
90	68	22
	Average	8
	Std.dev.	11.69995
	Std. Error	3.69985

Average = = 8

standard Deviation = sd = 11.70

standard error = sed = sd/sqrt(n) = 11.70/sqrt(10) = 3.7

Test statistic

t = 8/3.7 =  2.16225

dF = n -1 = 10 -1 = 9

tcritical  = TINV(0.10, 9) = 1.833

here t > tcritical so we would reject the null hypothesis.

Option A is correct here.