Discuss the below:
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.
b. Find a 95% confidence interval for the true population proportion of light bulbs that will last more than 500 hours.
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.
b. Construct a 99 percent confidence interval for the mean commission earned by local Tupperware dealers. You may assume the commissions are normally distributed.
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.
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. A 99% confidence interval (in inches) for the mean height of a population is 65.2 <μ < 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.
b. Use the values you found in part a to calculate the 95% confidence interval.