Several years ago, 47% of parents who had children in grades K-12 were satisfied

Question

Several years ago, 47% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,055 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,055 surveyed, 473 indicated that they were satisfied. Construct a 99% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed. 1. What are the null and alternative hypotheses? 2. Find the 99% confidence interval.

Explanation / Answer

1)

Ho: p = 0.47
Ha: p=/= 0.47

2)

First, we get the point estimate of the proportion, p^,              
              
p^ = x / n =    0.448341232          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p(1 - p) / n] =    0.015365993          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp   0.408761057          
upper bound = p^ + z(alpha/2) * sp =    0.487921408          
              
Thus, the confidence interval is              
              
(   0.408761057   ,   0.487921408   ) [ANSWER, CONFIDENCE INTERVAL]

As 0.47 is inside this interval, then there is no significant evidence that parents' attitudes toward the quality of education have changed. [CONCLUSION]

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