CB.Stats.UNC-4.Q: Determine the margin of error for a given sample size for a one-sample t-interval.

Determine the margin of error for a given sample size for a one-sample t-interval.

Example Problems

A Pokémon card distributor wants to estimate the mean weight in grams of unopened booster packs from a new set. They'll sample

n

packs to build a

95\%

confidence interval for the mean with a margin of error of no more than

0.4

grams. Preliminary data suggests that

\sigma = 2\text{ g}

is a reasonable estimate for the standard deviation of pack weights.

What is the smallest approximate sample size required to obtain the desired margin of error?

A soccer coach wants to estimate the mean distance in meters that her midfielders kick the ball during goal kicks. She'll sample

n

goal kicks to build a

90\%

confidence interval for the mean with a margin of error of no more than

3\text{ meters}

. Preliminary data suggests that

\sigma = 12\text{ meters}

is a reasonable estimate for the standard deviation.

What is the smallest approximate sample size required to obtain the desired margin of error?

A swim coach wants to estimate the mean 50-meter freestyle time in seconds for swimmers at a regional meet. She'll sample

n

swims to build a

95\%

confidence interval for the mean with a margin of error of no more than

0.5\text{ seconds}

. Preliminary data suggests that

\sigma = 3\text{ seconds}

is a reasonable estimate for the standard deviation of these times.

What is the smallest approximate sample size required to obtain the desired margin of error?

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