.A population has standard deviation ? = 17.3. a. How large a sample must be drawn so that a 95% confidence interval for ? will have a margin of error equal to 1.4? b. If the required confidence level were 98%, would the necessary sample size be larger or smaller?
1.A population has standard deviation ? = 17.3.
a. How large a sample must be drawn so that a 95%
confidence interval for ? will have a margin of error
equal to 1.4?
b. If the required confidence level were 98%, would the
necessary
2. Babies: According to the National Health Statistics Reports,
a sample of 360 one-year-old baby boys in the United States
had a mean weight of 25.5 pounds. Assume the population
standard deviation is ? = 5.3 pounds.
a. Construct a 95% confidence interval for the mean
weight of all one-year-old baby boys in the United
States
b. Should this confidence interval be used to estimate the
mean weight of all one-year-old babies in the United
States? Explain.
c. Based on the confidence interval constructed in part (a),
is it likely that the mean weight of all one-year-old boys
is less than 28 pounds?
3. Different standard deviations: Maria and Bob are going to
construct confidence intervals from different simple random
samples. Both confidence intervals will have level 95%.
Maria’s sample comes from a population with standard
deviation ? = 1, and Bob’s comes from a population with
? = 2. Both sample sizes are the same.
a. Which confidence interval will have the larger margin of
error? Or will they both be the same?
b. Which confidence interval is more likely to cover the
population mean? Or are they both equally likely to
do so?
4. Don’t construct a confidence interval: A college alumni
organization sent a survey to all recent graduates to ask their
annual income. Twenty percent of the alumni responded,
and their mean annual income was $40,000. Assume the
population standard deviation is ? = $10,000. Explain why
these data should not be used to construct a confidence
interval for the mean annual income of all recent graduates
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