Exam 7: Sampling Methods and the Central Limit Theorem

(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 systematic sampling. (iii) The mean of a population is called a parameter.

As the size of the sample increases, what happens to the shape of the sampling means?

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 4% underweight. The foreman samples 60 bags with each shipment and if the bags average more than 4% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

Mileage tests were conducted on a randomly selected sample of 100 newly developed automobile tires. The average tread wear was found to be 50,000 miles with a standard deviation of 3,500 miles. What is the best estimate of the average tread life in miles for the entire population of these tires?

The mean of all possible sample means is equal to the

We wish to study the advertising expenditures for the 200 largest companies in Canada. Suppose the objective of the study is to determine whether firms with high returns on equity (a measure of profitability) spent more of each sales dollar on advertising than firms with a low return or deficit. To make sure that the sample is a fair representation of the 200 companies, the companies are grouped on percent return on equity What is this type of sampling called?

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 $1,500 per month? The standard deviation of the sample is $300.

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

Alpha Corporation receives a shipment of flour every morning from their supplier. The flour is in 40 kg bags and Alpha will reject any shipment that is more than 5% underweight. The foreman samples 60 bags with each shipment and if the bags average more than 5% underweight, the whole shipment is returned to the supplier. Determine the value for the standard error of the proportion.

(i. As the sample size (n) increases, the spread in the distribution of the sample means decreases. (ii) If the sampling size equals the population size, the sampling error is 1. (iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

The Intelligence Quotient (IQ) test scores are normally distributed with a mean of 100 and a standard deviation of 15. i. What is the probability that a person would score between 85 and 115? ii. Given a class with 25 students, what is the probability that the class' average IQ score is between 85 and 115?

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 3 or more parts out of a sample of 50 to be defective?

(i. The standard error of the mean is the standard deviation of the sampling distribution of the sample means. (ii) The standard deviation of the sampling distribution of the mean is always smaller than the standard deviation of the population under study. (iii) For a sampling distribution of the means, 95% of the means would be between $\pm$ 1.96 standard deviations.

(i. For populations scattered in a wide area, the preferred technique for sampling is cluster 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.

Suppose a research firm conducted a survey to determine the average amount of money steady smokers spend on cigarettes during a week. A sample of 100 steady smokers revealed that the sample mean is $20 and the sample standard deviation is $5. What is the probability that a sample of 100 steady smokers spend between $19 and $21?

The daily sales of a small retail store in Toronto for the last 365 days are normally distributed with a mean of $2,050, and a standard deviation of $300. i. What is the probability of daily sales exceeding $2,500? ii. From a sample of 49 days, what is the probability of having a sample mean less than $2,500?

A new extended-life light bulb has an average service life of 750 hours, with a standard deviation of 50 hours. The shape of this distribution is unknown. From a sample of 100 light bulbs, about what percent of the bulbs will last more than 700 hours?

It has been estimated that 25% of all university students switch majors within their first two years of starting classes. If a random sample of 500 third-year students is taken at a city university, what is an estimate of the probability that 20% or more had switched majors within their first two years?

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 probability of finding a sample mean less than 80 minutes?

What is the difference between a sample mean and the population mean called?