Exam 7: Sampling and Sampling Distributions

Random samples of size 525 are taken from a process (an infinite population) whose population proportion is 0.3. The standard deviation of the sample proportions (i.e., the standard error of the proportion) is

Thirty percent of a magazine's subscribers are female. A random sample of 50 subscribers is taken. Answer the following questions using Excel. a.What is the probability that the proportion of females from this sample is at most 0.25? b.What is the probability that the proportion of females from this sample is between 0.22 and 0.28? c.What is the probability that the proportion of females from this sample is within .03 of the population proportion?

A sample statistic, such as , that estimates the value of the corresponding population parameter is known as a

From a population of 200 elements, the standard deviation is known to be 14. A sample of 49 elements is selected. It is determined that the sample mean is 56. The standard error of the mean is

A sample of 66 observations will be taken from a process (an infinite population). The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is

Missy Walters owns a mail-order business specializing in baby clothes. Missy is confident the dollar amounts of all her orders are normally distributed or nearly so. Assume she knows the mean and standard deviation are $249 and $46, respectively, for all orders she receives. a. Describe the sampling distribution of , where is the mean dollar-amount of an order for a sample of 10 orders. b. What is the probability that a simple random sample of 30 orders will provide an estimate of the population mean dollar-amount of an order that is within plus or minus $10 of the actual population mean? c. What happens to the sampling distribution of when the sample size is increased from 30 to 90? With a sample size of 90, what is the probability that will be between $239 and $259?

A population consists of 500 elements. We want to draw a simple random sample of 50 elements from this population. On the first selection, the probability of an element being selected is

The sample statistic s is the point estimator of

In a large university, 20% of the students are business majors. A random sample of 100 students is selected, and their majors are recorded. a.Compute the standard error of the proportion. b.What is the probability that the sample contains at least 12 business majors? c.What is the probability that the sample contains less than 15 business majors? d.What is the probability that the sample contains between 12 and 14 business majors?

The purpose of statistical inference is to provide information about the

Since the sample size is always smaller than the size of the population, the sample mean must

The sampling distribution of the sample mean

A random sample of nine telephone calls in an office provided the following information. a.Determine the point estimate for the average duration of all calls. b.What is the point estimate for the standard deviation of the population? c.What is the point estimate for the proportion of all calls that were long distance?

Stratified random sampling is a method of selecting a sample in which

A simple random sample of size n from a finite population of size N is to be selected. Each possible sample should have

The mean diameter of a ball bearing produced by a certain manufacturer is 0.80 cm with a standard deviation of 0.03 cm. A sample of 36 ball bearings is randomly selected from a production run. Use Excel to answer the following questions. a.What is the probability that the sample of ball bearings will have a mean less than 0.798 cm? b.What is the probability that the sample of ball bearings will have a mean of at least 0.815 cm? c.What is the probability that the sample of ball bearings will have a mean between 0.798 and 0.815 cm? d.For samples of size 36, 15% of all sample means are at most what diameter?

Excel's RAND function

A bank has kept records of the checking balances of its customers and determined that the average daily balance of its customers is $300 with a standard deviation of $48. A random sample of 144 checking accounts is selected. a.What is the probability that the sample mean will be more than $306.60? b.What is the probability that the sample mean will be less than $308? c.What is the probability that the sample mean will be between $302 and $308? d.What is the probability that the sample mean will be at least $296?

The price of a particular brand of jeans has a mean of $37.99 and a standard deviation of $7. A sample of 49 pairs of jeans is selected. Use Excel to answer the following questions. a.What is the probability that the sample of jeans will have a mean price less than $40? b.What is the probability that the sample of jeans will have a mean price between $38 and $39? c.What is the probability that the sample of jeans will have a mean price within $3 of the population mean?

There are 500 employees in a firm, 45% are female. A sample of 60 employees is selected randomly. a.Determine the standard error of the proportion. b.What is the probability that the sample proportion of females is between 0.40 and 0.55?