Several years ago, 50% 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 095 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 095 surveyed, 478 indicated that they were satisfied. Construct a 95% confidence interval to assess whether this represents evidence that parents' attitudes toward the quality of education have changed.

The 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

Step-by-step explanation:

We have to see if 50% = 0.5 is part of the confidence interval.

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:

95% 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 95% confidence interval for the proportion of parents that are satisfied with their children's education is (0.4118, 0.4618). 0.5 is not part of the confidence interval, so this represents evidence that parents' attitudes toward the quality of education have changed.

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