Question

a. A random sample of elementary school children in New York state is to be selected to estimate the proportion p who have received a medical examination during the past year. The survey found that x = 468 children were examined during the past year. Construct the 95 % confidence interval estimate of the population proportion p if the sample size was n=600 . Give your confidence interval bounds to at least 4 decimal places.

b) Which of the following is the correct interpretation for your answer in part (a)?
A. There is a 95% chance that the percentage of all elementary school children in NY who have received medical examination during the past year lies in the interval
B. We can be 95% confident that the percentage of elementary school children in the sample who have received medical examination during the last year lies in the interval
C. We can be 95% confident that the percentage of all elementary school children in NY who have received medical examination during the past year lies in the interval
D. None of the above

c. Under which of the following circumstances is it impossible to construct a confidence interval for the population mean?
A. A normal population with a small sample and an unknown population variance.
B. A non-normal population with a large sample and an unknown population variance.
C. A non-normal population with a small sample and an unknown population variance.
D. A normal population with a large sample and a known population variance.

d. A random sample of size n has been selected from a normally distributed population whose standard deviation is σ. In hypothesis testing for the population mean, the t-test should be used instead of the z-test if:
A. n>30 and σ is unknown
B. n<30and σ is known
C. both A and B are true
D. both A and B are false

Answer 1