Exam 7: Sampling Methods and the Central Limit Theorem

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 $80 and the sample standard deviation is $20. What is the probability that a sample of 100 steady smokers spend between $76 and $84?

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 retailer claims that 90% of its customers are "pleased" or "very pleased" with the customer service. In a survey of 300 customers taken last week, what is the probability that between 80% and 90% will be "pleased" or "very pleased" with the service?

The mean weight of trucks traveling on a particular section of I-475 is not known. A provincial highway inspector needs an estimate of the mean. He selects a random sample of 49 trucks passing the weighing station and finds the mean is 15.8 tonnes, with a standard deviation of the sample of 4.2 tonnes. What is probability that a truck will weigh less than 14.3 tonnes?

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?

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 18 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 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.

Sampling error is the difference between a corresponding sample statistic and the

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

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?

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 130 or more on the test? ii. You enrolled in a class of 25 students. What is the probability that the class' average IQ exceeds 130?

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?

If the sampling size equals the population size, what is the sampling error?

As the size of the sample increases, what happens to the shape of the sampling 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 is the probability that the mean completion time is between 1 and 2 hours, i.e., 60 and 120 minutes?

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 50 to be defective?

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 40 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.

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. What type of sampling is this?_____ sampling.

i. An estimate of the population mean based on a large sample is less reliable than an estimate made using a small sample. Ii) The standard error of the mean will vary according to the size of the sample that is in the denominator. As the sample size n gets larger, the variability of the sample means gets smaller. Iii) To determine the value of the standard error of the mean, the total error is divided by the sample size.

A convenience store estimates that 25% of its customers come in to buy milk. What is the probability that out of the next 200 customers, 60 or fewer will buy milk?