Several years ago 46 of parents who had children in grades K

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?

Solution

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   )

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Ho: p = 0.46

Ha: p =/ 0.46 [ANSWER]