Exam 7: Sampling and Sampling Distributions

Suppose the local Best Buy store averages 522 customers every day entering the facility with a standard deviation of 124 customers. A random sample of 40 business days was selected. What is the probability that the average number of customers in the sample is between 530 and 540?

A random sample of 49 cast aluminum pots is taken from a production line once every day. The number of defective pots is counted. The proportion of defective pots has been closely examined in the past and is believed to be 0.05. What are the upper and lower control limits for the chart?

We use a population parameter to make inferences about a sample statistic.

A preferred approach to quality control is the ________ approach.

Which of the following meets the requirements of a simple random sample?

According to the central limit theorem, the sampling distribution of approaches the normal distribution as the sample size ________.

The standard deviation of (standard error of the sample mean) equals the population standard deviation divided by the square root of the sample size, or, se( ) = equivalently.

Acceptance sampling is ________.

A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean?

The finite population correction factor for the standard error of the mean should be used when the ratio of the sample size to the size of population exceeds ________.

How does the variance of the sample mean compare to the variance of the population?

Bias refers to the tendency of a sample statistic to systematically over-or underestimate a population parameter.

A tutoring company claims that 75% of the high school students who hire one of their tutors will improve their grades. A) In a sample of 100 high school students, what is the probability that 80% or more improved their grades? B) In a sample of 200 high school students, what is the probability that 80% or more improved their grades? C) Comment on the reason for the difference between the computed probabilities in parts a and b.

Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000?

The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What is the probability that between 60% and 62.5% of those surveyed are members of the labor force?

A manufacturing process produces tubeless mountain bike tires in batches of 200. Past records show that 6% of the tires will not hold air. An engineer tests five batches, each one week apart, and shows the proportion of tires that will not hold air below. Proportion of tires that will not hold air: a. Construct the centerline and the upper control limit for the chart. B) Should the engineer be worried? Comment on any trend in the proportion of tubeless tires that will not hold air.

According to the 2011 Gallup daily tracking polls (www.gallup.com, February 3, 2012), Mississippi is the most conservative U.S. state, with 53.4 percent of its residents identifying themselves as conservative. What is the probability that at least 100 but fewer than 115 respondents of a random sample of 200 Mississippi residents identify as conservative?

According to the 2011 Gallup daily tracking polls (www.gallup.com, February 3, 2012), Mississippi is the most conservative U.S. state, with 53.4 percent of its residents identifying themselves as conservative. What is the probability that fewer than 45 respondents of a random sample of 100 Mississippi residents do not identify themselves as conservative?

The California Department of Education wants to gauge the difficulty of a new exam by having a sample of students at a particular school take the exam. The quality of the students at the chosen school varies widely and the school administrators are allowed to choose who gets to take the exam. The administrators have a strong incentive for the school to do well on the exam. Do you think the results will represent the true ability of the students at school? What kind of bias, if any, do you think will be present? Explain.

Cluster sampling is preferred when the objective is to increase precision.