Exam 7: Sampling Methods and the Central Limit Theorem

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.

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.

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.

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?

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 60 to be defective?

What type of sampling is it when a population is first divided into subgroups and then a sample is selected from each subgroup?

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?

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?

i. If a population is not normally distributed, the sampling distribution of the sample means tends to approximate a normal distribution. ii. The Central Limit Theorem states that if the sample size n is sufficiently large, the sampling distribution of the means will be approximately normal no matter whether the population is normally distributed, skewed, or uniform. Iii) Based on the sampling distribution of the means and the central limit theorem, the sample mean can be used as a good estimator of the population mean, assuming that the size of the sample is sufficiently large.

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 50 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.

Manufacturers were subdivided into groups by volume of sales. Those with more than $100 million in sales were classified as Class A large; those from $50 to $100 million as Class A medium size; and those between $25 and $50 million..., and so on. Samples were then selected from each of these groups. What is this type of sampling called?

An experiment involves randomly selecting a sample of 256 middle managers 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?

All possible samples of size n are selected from a population and the mean of each sample is determined. What is the mean of the sample means?

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 assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the average time to complete a tax form?

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?

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. 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

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

What shape will the sampling distribution of the mean be if a population is normally distributed?

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