Question

Several years​ ago, 37​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,065 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1,065 ​surveyed, 462 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.

4.   1-PropZ-interval

Confidence Interval  ______

                   

           => invnorm (_____, 0, 1) = ______

Answer 1

sample proportion, = 0.4338
sample size, n = 1065
Standard error, SE = sqrt(pcap * (1 - pcap)/n)
SE = sqrt(0.4338 * (1 - 0.4338)/1065) = 0.0152

Given CI level is 99%, hence α = 1 - 0.99 = 0.01
α/2 = 0.01/2 = 0.005, Zc = Z(α/2) = 2.58

Margin of Error, ME = zc * SE
ME = 2.58 * 0.0152
ME = 0.0392

CI = (pcap - z*SE, pcap + z*SE)
CI = (0.4338 - 2.58 * 0.0152 , 0.4338 + 2.58 * 0.0152)
CI = (0.3946 , 0.4730)

There is sufficient evidence because confidence interval doe snot contain 37%