Question

The superintendent of the Middletown school district wants to know which of the districts three schools has the lowest rate of parent satisfaction. He distributes a survey to 1,000 parents in each district which asks if the parent is satisfied with their child’s school, and all of these parents respond. Here are the results school

	school A	school B	school C	total
not satisfied	248	250	300	798
satisfied	752	750	700	2202
Total	1000	1000	1000	3000

a. Percentage the table in a way that best answers the superintendent’s question

b. Calculate the percentage point difference between the rate of satisfaction at school A and school B, between the rate of satisfaction at school A and school C, and between the rate of satisfaction at school B and school C. Explain what these numbers mean in English.

c. Calculate the chi square value of this table

d. Are the differences shown in this table statistically significant at the 95% level?

e. Based on what you found in (b) and (d), and using your own judgement, how would you answer the superintendent’s question?

Answer 1

a. Percentage the table in a way that best answers the superintendent’s question

Ans: Percentage the table in a way that best answers the superintendent’s question is

	school A	school B	school C
satisfied	75.2	75	70

b. Calculate the percentage point difference between the rate of satisfaction at school A and school B, between the rate of satisfaction at school A and school C, and between the rate of satisfaction at school B and school C. Explain what these numbers mean in English.

Ans: The percentage point difference between the rate of satisfaction at school A and school B

= 75.2%-75%=0.2%

The percentage point difference between the rate of satisfaction at school A and school C

=75.2%-70%=5.2%

The percentage point difference between the rate of satisfaction at school B and school C

=75%-70%=5%.

c. Calculate the chi square value of this table

Ans:

	Observed (O)
	school A	school B	school C	total
satisfied	752	750	700	2202
	Expected ( E)
	school A	school B	school C
satisfied	734	734	734
	(O-E)^2/E
	school A	school B	school C	total
satisfied	0.44141689	0.3487738	1.5749319	2.3651

The estimated Chi-square value is 2.3651 with 3-1=2 degree of freedom.

d. Are the differences shown in this table statistically significant at the 95% level?

Ans: The P-values of the Chi-square value=2.3651 for 2 degrees of freedom is 0.3065 and more than 0.05 level of significance. Hence, we can conclude that the differences in satisfaction between the schools by parents are statistically insignificant in this table at 0.05 level of significance ( at the 95% level).

. Based on what you found in (b) and (d), and using your own judgement, how would you answer the superintendent’s question?

Ans: From b) and d) we know that even there is 5% difference between A & C and B & C in b) the significant are insignificant from the table in d).