Question

Several years​ ago, 43​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,115 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1,115 surveyed, 466 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.

What are the null and alternative​ hypotheses?

Use technology to find the 99​% confidence interval.

The lower bound is __

The upper bound is__

What is the correct​ conclusion?

Answer 1

H₀: P = 0.43

H₁: P 0.43

= 466/1115 = 0.4179

At 99% confidence interval the critical value is z_0.005 = 2.58

The 99% confidence interval is

+/- z_0.005 * sqrt((1 - )/n)

= 0.4179 +/- 2.58 * sqrt(0.4179 * (1 - 0.4179)/1115)

= 0.4179 +/- 0.0381

= 0.3798, 0.4560

The lower bound = 0.3798

The upper bound = 0.4560

Since the interval contains the hypothesized value 0.43, so we should not reject the null hypothesis.

There is not sufficient evidence to conclude that parents attitude toward the quality of education have changed.