Some optometrists argue that as many as 25% of the elementary school children may have impaired vision. A random sample of 256 elementary school children was obtained, and each was given a vision test. Fifty were found to base some form of impaired vision. a) Is the sample size large enough to construct a confidence interval for p? b) Construct a 95% confidence interval for р. c) is there any evidence to suggest that the optometrists' claim of p= 0.25 is wrong? Justify your answer.

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Some optometrists argue that as many as 25% of the elementary school children may have impaired
vision. A random sample of 256 elementary school children was obtained, and each was given a vision
test. Fifty were found to base some form of impaired vision.
a) Is the sample size large enough to construct a confidence interval for p?
b) Construct a 95% confidence interval for p.
c) is there any evidence to suggest that the optometrists' claim of p= 0.25 is wrong? Justify your answer.
d) hat assumptions arc necessary to ensure the validity of this confidence interval?
Transcribed Image Text:Some optometrists argue that as many as 25% of the elementary school children may have impaired vision. A random sample of 256 elementary school children was obtained, and each was given a vision test. Fifty were found to base some form of impaired vision. a) Is the sample size large enough to construct a confidence interval for p? b) Construct a 95% confidence interval for p. c) is there any evidence to suggest that the optometrists' claim of p= 0.25 is wrong? Justify your answer. d) hat assumptions arc necessary to ensure the validity of this confidence interval?
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