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Confidence Interval: Mean & Proportion

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1. Out of a sample of 459 randomly selected light bulbs tested in a laboratory, 291 lasted more than 500 hours.

a. Find a 90% confidence interval for the true population proportion of light bulbs that will last more than 500 hours. (5 points)
b. Find a 95% confidence interval for the true population proportion of light bulbs that will last more than 500 hours. (5 points)

2. A random sample of the commissions earned by local Tupperware dealers last month is given below.

\$4377.47 \$3183.76 \$1970.16 \$2270.88 \$3860.06
\$2508.55 \$1569.64 \$4205.30 \$1663.68 \$3960.71

a. Find x-bar and s for this data set. (5 points)
b. Construct a 99 percent confidence interval for the mean commission earned by local Tupperware dealers. You may assume the commissions are normally distributed. (5 points)

3. Using census records a random sample of annual salaries of 45 adults living in one town was collected. The sample had a mean of \$22,298 and a standard deviation of \$14,200. Find a 95% confidence interval for the true mean annual salary for all adults living in the town. (5 points)

4. A savings and loan association needs information concerning the checking account balances of its local customers. A random sample of 14 accounts was checked and yielded a mean balance of \$644.14 and a standard deviation of \$297.29. Find a 98% confidence interval for the true mean checking account balance for local customers. You may assume balances are normally distributed. (5 points)

5. A 99% confidence interval (in inches) for the mean height of a population is 65.2 < &#956; < 66.8. This result is based on a sample size of 144. Construct a 95% confidence interval.

a. You will first need to find the sample mean and sample standard deviation based on the confidence interval given. (5 points)
b. Use the values you found in part a to calculate the 95% confidence interval. (5 points)