Question

We want to know if people feel hopeful about the future for different age groups. We conduct a survey on a scale of 1 (feel extremely unsecure) to 7 (feel extremely secure). The results are shown in Table 1.

Table 1: Feeling Secure about the Future
Young Adults		Adults		Elderly
1		5		7
2		5		6
3		4		7
3		2		6
4		2		6

A Find the F-ratio at the α = .05. Round to three numbers after the decimal point if possible (i.e., .123).

B.Do you retain or reject the null from part A? Why?

C.Perform a post-hoc test at the α = .05 to see which age groups are significantly different from each other (Tukey’s HSD).

Answer 1

excel<data<data analysis<one way anova

SUMMARY
Groups	Count	Sum	Average	Variance	standard deviation
Column 1	5	13	2.6	1.3	1.140175425
Column 2	5	18	3.6	2.3	1.516575089
Column 3	5	32	6.4	0.3	0.547722558
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Between Groups	38.8	2	19.4	14.92308	0.000556102	3.885294
Within Groups	15.6	12	1.3
Total	54.4	14
post-hoc test
group	difference	p-value
group1-group2	1	0
group1-group3	3.8	0.005
group2-group3	2.8	0.0052

A) null and alternate hypothesis:

H0:

H1: atleast one mean is different from other

i) test statistics

F =14.923

B) p-value = 0.0005

since p-value is less than level of significance so we reject the null hypothesis.

C) from post hoc test

group1-group2 is different means

group1-group3 is diferent mean

group2-group3 is different mean.