Practice Problems

\(\textbf{1)}\) We measure the lengths of 40 randomly chosen pieces of lumber, and get a mean length of 96 inches. The standard deviation of the length of lumber is .4 inches. Find the 95% confidence interval for the true mean length of the lumber.

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The answer is \(\text{from } 95.88 \text{ to } 96.12 \left(96 \pm 1.96 \cdot \frac{.4}{\sqrt{40}} \right)\)

\(\textbf{2)}\) We measure the weights of 36 randomly chosen statues, and get a mean weight of 15 lbs. The standard deviation of the weight of a statue is .6 lbs. Find the 90% confidence interval for the true mean weight of the statues.

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The answer is \(\text{from } 14.84 \text{ to } 15.16 \left(15 \pm 1.645 \cdot \frac{.6}{\sqrt{36}} \right)\)

\(\textbf{3)}\) We measure the weights of 55 randomly chosen oranges, and get a mean weight of 2 lbs. The standard deviation of the weight of an orange is .2 lbs. Find the 99% confidence interval for the true mean weight of the oranges.

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The answer is \(\text{from } 1.931 \text{ to } 2.069 \left(2 \pm 2.576 \cdot \frac{.2}{\sqrt{55}} \right)\)

See Related Pages\(\)

\(\bullet\text{ Confidence Interval Calculator}\)
\(\,\,\,\,\,\,\,\,\text{(Statskingdom.com)}\)

\(\bullet\text{ Statistics Homepage}\)
\(\,\,\,\,\,\,\,\,\text{All the Best Topics…}\)

\(\bullet\text{ Margin of Error}\)
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\(\bullet\text{ Confidence Intervals}\)
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\(\bullet\text{ Standard Error}\)
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\(\bullet\text{ Confidence Level}\)
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\(\bullet\text{ Type I and Type II Errors}\)
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\(\bullet\text{ One Sample z-test}\)
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\(\bullet\text{ Two Sample z-test for Difference Between Means}\)
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\(\bullet\text{ Hypothesis Test- Difference Between Proportions}\)
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\(\bullet\text{ Chi-squared test}\)
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