Question

Several years​ ago, 42​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive. A recent poll asked 1 comma 055 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 055 ​surveyed, 452 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? Upper H 0​: p ▼ greater than not equals less than equals nothing versus Upper H 1​: p ▼ greater than not equals less than equals nothing ​(Round to two decimal places as​ needed.)

Answer 1

Sample proportion = 452 / 1055 = 0.428

99% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.428 - 2.576 * sqrt [ 0.428 * ( 1 - 0.428) / 1055 ] < p < 0.428 + 2.576 * sqrt [ 0.428 * ( 1 - 0.428) / 1055 ]

0.389 < p < 0.467

99% CI is ( 0.389 , 0.467 )

The null and alternative hypothesis are

H0: p = 0.42

Ha: p 0.42