Exam 7: Sampling and Sampling Distributions

Exhibit 7-5 Random samples of size 17 are taken from a population that has 200 elements, a mean of 36, and a standard deviation of 8. -Refer to Exhibit 7-5. The mean and the standard deviation of the sampling distribution of the sample means are

Students of a large university spend an average of $5 a day on lunch. The standard deviation of the expenditure is $3. A simple random sample of 36 students is taken. a.What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b.What is the probability that the sample mean will be at least $4? c.What is the probability that the sample mean will be at least $5.90?

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 standard deviation of a point estimator is the

The probability distribution of all possible values of the sample mean is called the

As the sample size increases, the variability among the sample means

A sample of 8 new models of automobiles provides the following data on highway miles per gallon. Use Excel to answer the questions that follow the data. a.What is the point estimate for the average highway miles per gallon for all new models of autos? b.Determine the point estimate for the standard deviation of the population.

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 expected value of equals the mean of the population from which the sample is drawn

The set of all elements of interest in a study is

A population of size 1,000 has a proportion of 0.5. Therefore, the proportion and the standard deviation of the sample proportion for samples of size 100 are

The fact that the sampling distribution of the sample mean can be approximated by a normal probability distribution whenever the sample size is large is based on the

From a population of 500 elements, a sample of 225 elements is selected. It is known that the variance of the population is 900. The standard error of the mean is approximately

Whenever the population has a normal probability distribution, the sampling distribution of is a normal probability distribution for

A simple random sample of 28 observations was taken from a large population. The sample mean equaled 50. Fifty is a

Random samples of size 81 are taken from a process (an infinite population) whose mean and standard deviation are 200 and 18, respectively. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are

A theorem that allows us to use the normal probability distribution to approximate the sampling distribution of sample means and sample proportions whenever the sample size is large is known as the

Consider a population of five weights identical in appearance but weighing 1, 3, 5, 7, and 9 ounces. a.Determine the mean and the variance of the population. b.Sampling without replacement from the above population with a sample size of 2 produces ten possible samples. Using the ten sample mean values, determine the mean of the population and the variance of c.Compute the standard error of the mean.

Exhibit 7-3 The following information was collected from a simple random sample of a population. -Refer to Exhibit 7-3. The point estimate of the population standard deviation is

The sample statistic s is the point estimator of