Question

**BY HAND** For the Data Below, please do the following:

State the null and alternative hypotheses. (2 points)

Construct an ANOVA table (20 pts)

Determine whether your results are significant (1 points)

Do a post hoc analysis (using Tukey’s HSD), if necessary (5 points)

State your conclusions in one or two sentences. (2 points)

A survey was done in a community in which residents were asked if they felt that family planning counseling was needed in the community. The tabulation in the accompanying table gives the opinions and the number of children of the respondents. Determine whether there is a difference in mean number of children of respondents. Make sure you follow all the steps of hypothesis testing.

Table 1. Number of children among respondents, by perceived need for family planning counseling in the community

	Great Need	Some Need	No Need
	0	10	17
	1	5	10
	3	7	9
Number of children	4	3	3
	2	9	15
	1	8	10
	3	7	11
	0	9	10
	1	10	9
	2	9	8
Σx	17	77	102	196 (grand total)
x	1.7	7.7	10.2	6.53 (grand mean)

Answer 1

a) H0: There is no significant difference between means of Great need, Some need and No Need

H1: There is significant difference between means of Great need, Some need and No Need

b)

											Total	Ti^2/ni
Great Need	0	1	3	4	2	1	3	0	1	2	17	28.9
Some Need	10	5	7	3	9	8	7	9	10	9	77	592.9
No Need	17	10	9	3	15	10	11	10	9	8	102	1040.4
										Total G	196	1662.2

Sum of square =

1854 One-way ANOVA: Great Need, Some Need, No Neet Source DF      SS      MS      F      P Factor   2 381.67 190.83 26.86 0.000 Error   27 191.80    7.10 Total   29 573.47 S = 2.665   R-Sq = 66.55%   R-Sq(adj) = 64.08% c) P - Value < alpha (0.05), we reject H0 Thus, we conclude that There is significant difference between means of Great need, Some need and No Need d) Level               N    Mean StDev Great Need     10   1.700 1.337 Some Need    10   7.700 2.263 No Neet      10 10.200 3.795 t critical value = 3.506 Test statistic of M1 and M2 is 7.118 > T critical value(3.506), So there is significance difference between means of M1 an dM2 Test statistic of M2 and M3 is 2.966 < T critical value(3.506), So there is no significance difference between means of M2 an dM3 Test statistic of M1 and M3 is 10.085 > T critical value(3.506), So there is significance difference between means of M1 an dM3 Please give thumbs up to my answer...!!