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2 answers:
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Answer:
a)
, in which z is related to the confidence level.
b) A sample size of 991 is needed.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of , and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of .
The margin of error is:
In 16% of all homes with a stay-at-home parent, the father is the stay-at-home parent
This means that
a. What sample size is needed if the research firm's goal is to estimate the current proportion of homes with a stay-at-home parent in which the father is the stay-at-home parent with a margin of error of 0.03 (round up to the next whole number).
This is n for which . So
, in which z is related to the confidence level.
Question b:
99% confidence level,
So , z is the value of Z that has a pvalue of
, so
.
Rounding up
A sample size of 991 is needed.