Exam 7: Sampling Methods and the Central Limit Theorem

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?

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. Iii) Ontario Parks wardens estimate the average weight of the fish or game population by using creel checks and other devices. Based on this sample data, a warden might estimate that the mean weight of Coho salmon caught in Lake Ontario is 2.5 pounds. This single number is called a point estimate of The unknown population parameter.

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?

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

Which sampling method would be best to use if the population can be divided into homogeneous subgroups?

A study of a company's practice regarding the payment of invoices revealed that on the average an invoice was paid 20 days after it was received. The standard deviation equalled five days. A sample of 25 invoices is selected. Assuming that the distribution is normal, what percent of the sampled invoices were paid within 15 days of receipt?

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?

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?

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 that average student study time is between 18 and 22 hours?

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 36 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. It is often not feasible to study the entire population because it is impossible to check all the items in the population. ii. Sampling a population is often necessary because the cost of studying all the items in the population is prohibitive. Iii) Sampling is a sign of laziness on the part of the statistician.

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 60 to be defective?

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 that a sample mean would exceed 20 hours per week?

For populations scattered in a wide area, what is the preferred technique for sampling?

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?

Which sampling method would you use if every k-th item in the population sequence is selected?

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 50 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.

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 that the mean completion time will be more than 120 minutes?

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.