Let p be the population proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive.
Set of hypothesis :
Confidence interval for population proportion is given by :-
, where
n= sample size
= sample proportion
and is the two-tailed z-value for confidence level (c).
As per given ,
Sample size of parents : n= 1085
Number of parents indicated that they were satisfied= 466
Sample proportion :
Critical value for 90% confidence interval : ( by z-value table)
Now, the 90% confidence interval :
Thus , the 90% confidence interval: (0.4043, 0.4537).
Since 0.43 lies in 90% confidence interval , it means we do not have enough evidence to reject the null hypothesis .
i.e. We are have no evidence that parents' attitudes toward the quality of education have changed.