Several years ago, 46% of parents who had children in grades K-12 were satisfied

Question

Several years ago, 46% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,005 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,005 surveyed, 486 indicated that they were satisfied. Construct a 99% confidence interval to assess whether this represents evidence that parents’ attitudes towards the quality of education have changed.

What are the null and alternative hypotheses?

Explanation / Answer

First, we get the point estimate of the proportion, p^,              
              
p^ = x / n =    0.48358209          
              
Also, we get the standard error of p, sp:              
              
sp = sqrt[p(1 - p) / n] =    0.015721456          
              
Now, for the critical z,              
alpha/2 =   0.005          
Thus, z(alpha/2) =    2.575829304          
Thus,              
              
lower bound = p^ - z(alpha/2) * sp   0.443086302          
upper bound = p^ + z(alpha/2) * sp =    0.524077877          
              
Thus, the confidence interval is              
              
(   0.443086302   ,   0.524077877   )

*************************************

Ho: p = 0.46

Ha: p =/ 0.46 [ANSWER]

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