Week 7: Sampling Distributions

If the variance of a population is 10, then the variance of the mean for an SRS (Simple Random Sample) of 30 observations from this population will be  $\frac{10}{\sqrt{30}}$ . 

• True

• False

The central limit theorem states that for large n, µ is approximately Normal.

• True

• False

Identify the type of sampling design in the following situation:

Suppose you are selecting microchips from a production line for inspection for bent probes. As the chips proceed past the inspection point, every 100th chip is selected for inspection.

• Systematic Random Sampling

• Simple Random Sampling

• Cluster Sampling

• Stratified Random Sampling

Identify the type of sampling design in the following situation:

The USDA inspects produce for E. coli contamination. As trucks carrying produce cross the border, the truck is stopped for inspection. A random sample of five containers is selected for inspection from the hundreds of containers on the truck. Every apple in each of the five containers is then inspected for E. coli.

• Stratified Random Sampling

• Systematic Random Sampling

• Simple Random Sampling

• Cluster Sampling

Identify the type of sampling design in the following situation:

The Internal Revenue Service wants to estimate the amount of personal deductions taxpayers made based on the type of deduction: home office, state income tax, property taxes, property losses, and charitable contributions. The amount claimed in each of these categories varies greatly depending on the adjusted gross income of the taxpayer. Therefore, a simple random sample would not be an efficient design. The IRS decides to divide taxpayers into five groups based on their adjusted gross incomes and then takes a simple random sample of taxpayers from each of the five groups.

• Simple random sampling

• Cluster Sampling

• Stratified Random Sampling

• Systematic Random Sampling

• SRS

What is the name given to the standard deviation of the distribution of sample means? (hint: two words)

 A random sample of n = 100 observations is selected from a population with µ = 30 and σ = 16. Find: $P\left(22.1\ <\ \overline{x}\ <\ 26.8\right)$ 

• 0.6446

• 0.9772

• 0.0456

• 0.0228

Majesty Video Production Inc. wants the mean length of its advertisements to be 30 seconds. Assume the distribution of ad length follows the normal distribution with a population standard deviation of 2 seconds. Suppose we select a sample of 16 ads produced by Majesty.

What percent of the sample means will be between 29.75 and 31.0 seconds?

• 46.8

• 56.8

• 66.9

• 34.5

Information from the American Institute of Insurance indicates the mean amount of life insurance per household in the United States is $165,000. This distribution follows the normal distribution with a standard deviation of $40,000.

If we select a random sample of 49 households, what is the probability of selecting a sample with a mean of at least $167,000? Round your answer to one decimal value.

According to an IRS study, it takes a mean of 330 minutes for taxpayers to prepare, copy, and electronically file a 1040 tax form. This distribution of times follows the normal distribution and the standard deviation is 80 minutes. A consumer watchdog agency selects a random sample of 40 taxpayers.

What is the probability the sample mean is greater than 320 minutes? Round your answer to two decimals.