Question

Several years ago, 45% ofparents 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 1,005 surveyed, 453 indicated that they were satisfied. Construct a 90% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.

1. What are the null and alternative hypotheses?

2. Find the 90% confidence interval.

3. What conclusions can be made.

Answer 1

a)

H0: p = 0.45

Ha: p 0.45

b)

90% confidence interval is

p̂ = X / n = 453/1005 = 0.451
p̂ ± Z(α/2) √( (p * q) / n)
0.451 ± Z(0.1/2) √( (0.4507 * 0.5493) / 1005)
Z(α/2) = Z(0.1/2) = 1.645
Lower Limit = 0.451 - Z(0.1) √( (0.4507 * 0.5493) / 1005) = 0.425
upper Limit = 0.451 + Z(0.1) √( (0.4507 * 0.5493) / 1005) = 0.477
90% Confidence interval is ( 0.425 , 0.477 )

c)

Since 0.45 contained in confidence interval , we fail to reject null hypothesis.

We conclude that we do not have sufficient evidence to support the claim that parents' attitudes

toward the quality of education have changed.