Question

Several years​ ago, 54​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,015 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1,015 surveyed, 495 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?

The lower bound is

The upper bound is

Answer 1

H₀: P = 0.54

H₁: P 0.54

= 495/1015 = 0.49

At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval is

+/- z_0.025 * sqrt((1 - )/n)

= 0.49 +/- 1.96 * sqrt(0.49 * (1 - 0.49)/1015)

= 0.49 +/- 0.031

= 0.459, 0.521

Since the confidence interval doesn't contain the hypothesized value 0.54, so we should reject the null hypothesis.

There is sufficient evidence to conclude that parent's attitudes towards the quality of education have changed.