Question

#22 Several years​ ago, 39​% 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 115 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 115 ​surveyed, 498 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. What are the null and alternative​ hypotheses? Upper H 0​: p ▼ greater than equals not equals less than nothing versus Upper H 1​: p ▼ equals greater than less than not equals nothing ​(Round to two decimal places as​ needed.) Use technology to find the 90​% confidence interval. The lower bound is nothing. The upper bound is nothing. ​(Round to two decimal places as​ needed.) What is the correct​ conclusion? A. Since the interval contains the proportion stated in the null​ hypothesis, there is sufficient evidence that​ parents' attitudes toward the quality of education have changed. B. Since the interval does not contain the proportion stated in the null​ hypothesis, there is insufficient evidence that​ parents' attitudes toward the quality of education have changed. C. Since the interval does not contain the proportion stated in the null​ hypothesis, there is sufficient evidence that​ parents' attitudes toward the quality of education have changed. D. Since the interval contains the proportion stated in the null​ hypothesis, there is insufficient evidence that​ parents' attitudes toward the quality of education have changed. Click to select your answer(s).

Answer 1

We want to test whether parents are satisfied or not, so it is a two tailed hypothesis

Use TI-84 calculator

press STAT then TESTS then 1-PropZInt

enter the data as follows

x = 498

n =1155

c level = 0.90

Press Enter, we get

90% confidence interval = (40.72, 45.51)

it is clear that the null value of 39% is not included in the confidence interval and both limits of confidence interval are higher than 39%, So we can say that the percentage has increased or changed

Option C is correct