Question

several years ago, 40% of parents with children in grades k - 12 were satisfied with the quality of education the students receive. a recent poll found that 453 of 1,145 parents with children in grades k - 12 were satisfied with the quality of education the students receive. construct a 95% confidence interval to assess whether this represents evidence that parents attitudes toward the quality of education have changed
click the icon to view the confidence interval critical value table
(type integers or decimals. do not round)
find the 95% confidence interval
the lower bound is 0.368
the upper bound is 0.424
(round to three decimal places as needed)
what is the correct conclusion?
a. 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.
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 contains 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.

Explanation:

In hypothesis testing using confidence intervals, if the hypothesized proportion (in this case, \(0.40\)) is not within the confidence interval, we reject the null hypothesis (which assumes no change in parents' attitudes). Here, the confidence interval is \(0.368\) to \(0.424\), and \(0.40\) is within this interval. When the hypothesized value is within the confidence interval, we fail to reject the null hypothesis, meaning there is insufficient evidence to conclude that parents' attitudes have changed.

Answer:

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.