Exam 7: Sampling Methods and the Central Limit Theorem

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?

(i. The type of sampling when a population is first divided into subgroups and then a sample is selected from each subgroup is called 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.

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. 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 zero. (iii) If a population is normally distributed, the sampling distribution of the mean is normally distributed.

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. From a sample of 49 days, what is the probability of having a sample mean more than $2,000?

What sample statistic is used to estimate a population parameter?

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?

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?

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?

70% of North American women have pierced ears. For a survey of 49 women, what is the standard error?

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?

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?

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 preparation time is between 80 and 90 minutes?

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 is the probability that a sample mean would exceed 90 minutes per filing?

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?

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 35 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. 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 larger 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.

For a population that is not normally distributed, the distribution of the sample means will:

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?