Exam 7: Sampling Distributions

A sampling distribution is a distribution for a statistic.

Suppose 10 for a population.In a sample where is randomly taken, 95% of all possible sample means will fall between 48.04 and 51.96.

SCENARIO 7-1 The time spent studying by students in the week before final exams follows a normal distribution with a standard deviation of 8 hours.A random sample of 4 students was taken to estimate the mean study time for the population of all students. -Referring to Scenario 7-1, what is the probability that the sample mean is more than 3 hours below the population mean?

Suppose for a population.In a sample where n = 100 is randomly taken, 95% of all possible sample means will fall above 76.08.

A study at a college in the west coast reveals that, historically, 45% of the students are minority students.If random samples of size 75 are selected, the standard error of the proportion of students in the samples who are minority students is _________.

The standard error of the sampling distribution of a sample proportion is where is the sample proportion.

The sample mean is an unbiased estimator for the population mean.

For sample size 1, the sampling distribution of the mean will be normally distributed

The standard error of the mean

For distributions such as the normal distribution, the arithmetic mean is considered more stable from sample to sample than other measures of central tendency.

A study at a college in the west coast reveals that, historically, 45% of the students are minority students.If a random sample of size 75 is selected, the probability is _______ that between 30% and 50% of the students in the sample will be minority students.

Which of the following statements about the sampling distribution of the sample mean is incorrect?

A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country has high-speed access to the Internet.Random samples of size 200 are selected from the country's population. -Referring to Scenario 7-5, what is the probability less than 20% of the entire population will have high-speed access to the Internet?

The standard error of the population proportion will become larger

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected.What is the standard error of the mean?

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past.Suppose a sample of 100 major league players was taken.What was the standard error for the sample mean salary?

SCENARIO 7-2 The mean selling price of new homes in a small town over a year was $115,000.The population standard deviation was $25,000.A random sample of 100 new home sales from this city was taken. -Referring to Scenario 7-2, what is the probability that the sample mean selling price was between $114,000 and $116,000?

The amount of time required for an oil and filter change on an automobile is normally distributed with a mean of 45 minutes and a standard deviation of 10 minutes.A random sample of 16 cars is selected.What is the probability that the sample mean will be between 39 and 48 minutes?

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. What percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?