Exam 7: Sampling Methods and the Central Limit Theorem

An experiment involves selecting a random sample of 256 middle managers at random for study. One item of interest is their mean annual income. The sample mean is computed to be $35,420 and the sample standard deviation is $2,050. What is the standard error of the mean?

(i. The type of sampling when a population is first divided into subgroups and then a sample is selected from each subgroup is called stratified random sampling. (ii) Auditors may select every 20th file starting with say, the 5th file in the top drawer. Then file numbers 25, 45, 65, 85, are audited. This type of sampling is called cluster sampling. (iii) The mean of a population is called a parameter.

(i. For populations scattered in a wide area, the preferred technique for sampling is simple random sampling. (ii) If the population can be divided into homogeneous subgroups, stratified random sampling is the best sampling method to use. (iii) If every k-th item in the population sequence is selected, you are using systematic random sampling.

i. A simple random sample assumes that each item or person in the population has an equal chance of being included. ii. We can expect some difference between sample statistics and the corresponding population parameters. This difference is called the sampling error. iii. A sampling distribution of the means is a probability distribution consisting of a list of all possible sample means of a given sample size selected from a population and the probability of occurrence associated with each sample mean.

GreenFacts, a non-profit organization, reports that the average adult in Europe consumed 17 litres of alcohol last year. The standard deviation is 2.1 litres. If we randomly select 42 European adults, what is the probability that the sample mean is more than 17.8 litres?

i. If probability sampling is done, each item in the population has a chance of being chosen. ii. If the size of a sample equals the size of the population, we would not expect any error in estimating the population parameter.

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 2 or more parts out of a sample of 60 to be defective?

A province-wide sample survey is to be made. First, the province is subdivided into counties. Seven counties are selected at random and further sampling is concentrated on these seven counties. What type of sampling is this?

What is it called when all the items in a population have a chance of being selected in a sample?

A group of statistics students decided to conduct a survey at their university to find the average (mean) amount of time students spend studying per week. Based on a simple random sample, they surveyed 144 students. The statistics showed that students studied an average of 20 hours per week with a standard deviation of 10 hours. What is the standard error of the mean?

Which of the following is the standard error of the mean?

70% of North American women have pierced ears. In a survey of 49 women, what is the probability that less than 30 had pierced ears?

Prince Edward Island Fisheries and Environment has been feeding a special food to rainbow trout fingerlings in a pond. A sample of the weights of 40 trout revealed that the mean weight is 402.7 grams and the standard deviation 8.8 grams. What is the probability that the mean weight for a sample of 40 trout exceeds 405.5 grams?

Dawson's Repair Service orders parts from an electronic company who advertises its parts o be no more than 2% defective. What is the probability that Bill Dawson finds 4 or more parts out of a sample of 50 to be defective?

Suppose we select every fifth invoice in a file. What type of sampling is this?

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be under $1,800 per month? The standard deviation of the sample is $300.

The mean rent for a two-bedroom apartment in the Greater Toronto Area is $2,000 per month. The distribution of the monthly costs does not follow the normal distribution. In fact, it is positively skewed. What is the probability of selecting a sample of 36 two-bedroom apartments and finding the mean to be at least $1,500 per month? The standard deviation of the sample is $300.

An accounting firm is planning for the next tax preparation season. From last year's returns, the firm collects a systematic random sample of 100 filings. The 100 filings showed an average preparation time of 90 minutes with a standard deviation of 140 minutes. What is the standard error of the mean?