Answer:
Step-by-step explanation:
Use the given conditions to to write the equation for the line in point-slope form and general form. passing through(9, -7) and
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The confidence interval for confidence level of is
where is the sample mean,
is the critical value for the given confidence level,
is the standard deviation of the population, and
is the sample size. The margin of error is the
term.
a) For a confidence level of , we have
. So in order to have a margin of error of at most 25 points, we have
so Raina should collect a sample of at least 269 students.
b) A confidence interval with a higher confidence level would more closely approximate and reflect the population, so it stands to reason that Luke should collect a larger sample than Raina to meet his 99% confidence spec.
c) For a confidence level of , we have
. Then the margin of error would at most satisfy
so that Luke should collect a sample of at least 666 students.