Several years ago, 54% of parents who had children in grades K-12 were satisfied

Question

Several years ago, 54% of parents who had children in grades K-12 were satisfied with the quality of education the students receive. A recent poll asked 1,035 parents who have children in grades K-12 if they were satisfied with the quality of education the students receive. Of the 1,035 surveyed, 491 indicated that they were satisfied. Construct a 99% 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?

a) Upper H0: p (>, ,=,< pick one)   #   versus Upper H1: p(>, ,=,< pick one)   #(Round to two decimal places as needed.)

b) P =

Explanation / Answer

Below are the null and alternate hypothesis
H0: p = 0.54
H2: p 0.54

For 99% CI, z=2.58

Margin of error, ME = z*sqrt(p*(1-p)/n)
ME = 2.58*sqrt(0.54*(1-0.54)/1035) = 0.04

pcap = 491/1035 = 0.4744
CI = (pcap - ME, pcap + ME) = (0.4744 - 0.04, 0.4744 + 0.04) = (0.5144, 0.4344)

As 0.54 does not lies within the confidence interval calculated, we rejected the null hypothesis. This means there is significant evidence that the attitude of parents had changed.

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