Question

Two sample T hypothesis test (show your work) (NO HAND WRITING ITS HARD TO READ)

A food allergy accident happen that many time per year. Come up with a null and alt,

looking at from 2005 to 2011 and 2012 to 2018.

2005	73
2006	63
2007	86
2008	78
2009	80
2010	82
2011	86
2012	87
2013	78
2014	53
2015	67
2016	50
2017	37
2018	8

Also have the fatal rate if you can tie that in some how? with another hypothesis test

Fatal
(2005)19
13
17
21
26
29
22
25
16
12
24
18
6
(2108)1

Answer 1

here we use t-test with

null hypothesis H0:µ1=µ2 and alternate hypothesis H1: µ1≠µ2

statistic t=|(mean1-mean2)|/((s_p*(1/n1 +1/n2)^1/2) with df is n=n1+n2-2 and s_p²=((n1-1)s1²+(n2-1)s2²)/n

(for allergy) two tailed p-value is less than typical level of significance alpha=0.05, so we reject the null hypothesis and conclude that period 2005-11 is different  than 2012-18

t-test
	sample	mean	s	s2	n	(n-1)s2
	2005-11	78.2900	8.1400	66.2596	7	397.5576
	2012-18	54.2900	26.6300	709.1569	7	4254.9414
	difference=	24.0000	sum=	775.4165	14	4652.4990
	sp2=	387.7083
	sp=	19.6903
	SE=	10.5249
	t=	2.2803
two tailed	p-value=	0.0417
two tialed critical	t(0.05)	2.1788

(for fatal)  two tailed p-value is more than typical level of significance alpha=0.05, so we accept the null hypothesis and conclude that period 2005-11 is not different  than 2012-18

t-test
	sample	mean	s	s2	n	(n-1)s2
	2005-111	21.0000	5.3900	29.0521	7	174.3126
	2012-18	14.5700	8.9000	79.2100	7	475.2600
	difference=	6.4300	sum=	108.2621	14	649.5726
	sp2=	54.1311
	sp=	7.3574
	SE=	3.9327
	t=	1.6350
two tailed	p-value=	0.1280
two tialed critical	t(0.05)	2.1788

year	allergy	fatal	year	allergy	fatal
2005	73	19	2012	87	25
2006	63	13	2013	78	16
2007	86	17	2014	53	12
2008	78	21	2015	67	24
2009	80	26	2016	50	18
2010	82	29	2017	37	6
2011	86	22	2018	8	1
n=	7	7	7	7	7
mean=	78.29	21.00		54.29	14.57
s=	8.14	5.39		26.63	8.90