Question

Several years​ ago, 48​% 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, 455 indicated that they were satisfied. Construct a 95​% confidence interval to assess whether this represents evidence that​ parents' attitudes toward the quality of education have changed.

What are the null and alternative​ hypotheses?

Answer 1

H0: p = 0.48

Ha: p 48

p̂ = X / n = 455/1055 = 0.431
p̂ ± Z(α/2) √( (p * q) / n)
0.431 ± Z(0.05/2) √( (0.4313 * 0.5687) / 1055)
Z(α/2) = Z(0.05/2) = 1.96
Lower Limit = 0.431 - Z(0.05) √( (0.4313 * 0.5687) / 1055) = 0.401
upper Limit = 0.431 + Z(0.05) √( (0.4313 * 0.5687) / 1055) = 0.461
95% Confidence interval is ( 0.401 , 0.461 )

Since proportion 0.48 not contained in confidence interval, we have sufficient evidence to

conclude that parents' attitudes toward the quality of education have changed.