Question

Several years​ ago, 35​% 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 145 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 145 ​surveyed, 465 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. What are the null and alternative​ hypotheses? Upper H 0​: p equals . 35 versus Upper H 1​: p not equals . 35 ​(Round to two decimal places as​ needed.) Use technology to find the 95​% confidence interval. The lower bound is nothing. The upper bound is nothing. ​(Round to two decimal places as​ needed.)

Answer 1

Given that, n = 1145 and x = 465

=> sample proportion = 465/1145 = 0.4061

The null and alternative hypotheses are,

H0 : p = 0.35

Ha : p ≠ 0.35

A 95% confidence level has significance level of 0.05 and critical value is,

The 95% confidence interval for the population proportion is,

​​​​​​

Therefore, the lower bound is 0.38 and the upper bound is 0.44