Question

Several years​ ago, 45​% 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 015 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1 comma 015 ​surveyed, 464 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. Use technology to find the 90​% confidence interval.

Answer 1

SOLUTION:

From given data,

Several years​ ago, 45​% of parents who had children in grades​ K-12 were satisfied with the quality of education the students receive.

A recent poll asked 1,015 parents who have children in grades​ K-12 if they were satisfied with the quality of education the students receive. Of the 1,015 ​surveyed, 464 indicated that they were satisfied.

Sample Proportion 1 () = 45% = 45/100 = 0.45

Sample size 1 () = 1015

Favorable cases () = 464

=   / = 464 / 1015 = 0.4571428

SP = sqrt ((1-) / n )

SP = sqrt (0.45(1-0.45) / 1015)

SP = 0.015615

90% confidence interval

Confidence interval is 90%

90% = 90/100 = 0.90

= 1 - Confidence interval = 1-0.90 = 0.10

/2 = 0.10 / 2

= 0.05

Z_/2 = Z_0.05 = 1.645

90% confidence interval for the proportion:

Z_/2 * SP

0.4571428 1.645 * 0.015615

0.4571428 0.025686675

(0.4571428 -0.025686675 , 0.4571428 +0.025686675)

(0.4314 , 0.4828)

Since confidence interval does not contain 45% so this represent evidence that parents attitude toward the quality of education have change.