Question

Several years​ ago,

3535​%

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 1951,195

parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the

1 comma 1951,195

​surveyed,

489489

indicated that they were satisfied. Construct a

9595​%

confidence interval to assess whether this represents evidence that​ parents' attitudes toward the quality of education have changed.

Answer 1

Given that, n = 1195 and x = 489

sample proportion = 489/1195 = 0.4092

The null and alternative hypotheses are,

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

The 95% confidence interval for p is,

Therefore, the 95% confidence interval is,

(38.13% , 43.71%)

Since, population proportion of 35% is not lies in above interval we can conclude that, there is sufficient evidence that​ parents' attitudes toward the quality of education have changed.