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 075 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 075 surveyed, 462 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.

The 90% confidence interval for the proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive is (0.405, 0.455). 0.42 = 42% is part of the confidence interval, so we are 90% sure that there is no evidence that parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of , we have the following confidence interval of proportions.

In which

z is the zscore that has a pvalue of .

For this problem, we have that:

90% confidence level

So , z is the value of Z that has a pvalue of , so .

The lower limit of this interval is:

The upper limit of this interval is:

The 90% confidence interval for the proportion of parents who had children in grades K-12 were satisfied with the quality of education the students receive is (0.405, 0.455). 0.42 = 42% is part of the confidence interval, so we are 90% sure that there is no evidence that parents' attitudes toward the quality of education have changed.