Exam 7: Sampling and Sampling Distributions

Suppose a population has a mean of 450 and a variance of 900.If a random sample of size 100 is drawn from the population, the probability that the sample mean is between 448 and 453 is closest to _______.

The sampling distribution of $\hat { p }$ is close to normal provided that n $\ge$ 30.

A sampling distribution is the distribution of a sample statistic such as the sample mean or sample proportion.

Suppose a population has a mean of 400 and a standard deviation of 24.If a random sample of size 144 is drawn from the population, the probability of drawing a sample with a mean less than 402 is closest to _______.

According to the central limit theorem, for samples of size 169 drawn from a population with μ = 1,014 and σ = 65, the standard deviation of the sampling distribution of sample means would equal _______.

Increasing the sample size causes the numerical value of standard error of the sample means to increase.

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system.If 10% of the 5,000 payroll vouchers issued since January 1, 2018, have irregularities, the probability that Pinky's random sample of 200 vouchers will have a sample proportion of between .06 and .14 is closest to ___________.

The sampling distribution of $\hat { p }$ has a mean equal to the square root of the population proportion p.

On Saturdays, cars arrive at David Zebda's Scrub and Shine Car Wash at the rate of 80 cars per hour during the ten-hour shift.David wants a sample of 40 Saturday customers to answer the long version of his quality service questionnaire.He randomly selects 9 as a starting point and instructs the crew to select the 9th customer and every 20^th customer thereafter (9, 29, 49, etc.).His sample is a __________.

If the population proportion is 0.90 and a sample of size 64 is taken, which is closest to the probability that the sample proportion is less than 0.88?

Pinky Bauer, Chief Financial Officer of Harrison Haulers, Inc., suspects irregularities in the payroll system.She knows that 2,500 payroll vouchers have been issued since January 1, 2018, and her staff doesn't have time to inspect each voucher.So, she randomly selects 53 as a starting point and orders her staff to inspect the 53rd voucher and each voucher at an increment of 100 (53, 153, 253, etc.).Her sample is a ___________.

The central limit theorem states that if the sample size, n, is large enough (n ≥20), the distribution of the sample means is normally distributed regardless of the shape of the population.

Paige DeMarco is the Vice President for University Advancement at State University.She is responsible for the capital campaign to raise money for the new student services building.Paige plans to target alumni and acquires her sampling frame from the State University Office of Alumni Relations.She intends to contact these individuals regarding possible donations.She randomly selects the sixth name as a starting point and then selects every 100th subsequent name (106, 206, 306, etc.).Her sample is a _________.

Catherine Chao, Director of Marketing Research, needs a sample of Kansas City households to participate in the testing of a new toothpaste package.If 40% of the households in Kansas City prefer the new package, the probability that Catherine's random sample of 300 households will have a sample proportion between 0.35 and 0.45 is closest to ___________.

The directory or map from which a sample is taken is called the census.

Financial analyst Larry Potts needs a sample of 100 securities listed on the New York Stock Exchange.The current issue of the Wall Street Journal has an alphabetical list of the 2,531 securities traded on the previous business day.Larry uses a table of random numbers to select 100 numbers between 1 and 2,531.His sample is a ____________.

Cluster (or area)sampling is a type of random sampling technique.

The two major categories of sampling methods are proportionate and disproportionate sampling.

A carload of steel rods has arrived at Cybermatic Construction Company.The car contains 50,000 rods.Claude Ong, Manager of Quality Assurance, directs his crew to measure the lengths of 100 randomly selected rods.If the population of rods has a mean length of 120 inches and a standard deviation of 0.05 inch, the probability that Claude's sample has a mean greater than 120.0125 inches is _____________.

According to the central limit theorem, if a sample of size 56 is drawn from a population with a mean of 16, the mean of all sample means would equal _______.