Exam 7: Sampling Distributions

For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off.This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes.Suppose100 flights have been randomly sampled.Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these100 flights.

Why is the Central Limit Theorem so important to the study of sampling distributions?

SCENARIO 7-6 Online customer service is a key element to successful online retailing.According to a marketing survey, 37.5% of online customers take advantage of the online customer service.Random samples of 200 customers are selected. -Referring to Scenario 7-6, % of the samples are likely to have between 35% and 40% who take advantage of online customer service.

At a computer manufacturing company, the actual size of a computer chip is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter.A random sample of 12 computer chips is taken.Above what value do 2.5% of the sample means fall?

A sample that does not provide a good representation of the population from which it was collected is referred to as a (n) sample.

The Central Limit Theorem is important in statistics because

An unbiased estimator will have a value, on average across samples, equal to the population parameter value.

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The sampling distribution of the sample mean will be approximately normal only if the population sampled is normal.

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, the standard error of all the sample proportions is .

If the expected value of a sample statistic is equal to the parameter it is estimating, then we call that sample statistic

SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4, 90% of the samples will have less than what percentage of customers who will make a purchase after visiting the web site?

A sample of size 25 provides a sample variance of 400.The standard error, in this case equal to 4, is best described as the estimate of the standard deviation of means calculated from samples of size 25.

The sample proportion is an unbiased estimate of the population proportion.

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 differs from the population mean by more than 3 hours?

The amount of bleach a machine pours into bottles has a mean of 36 oz.with a standard deviation of 0.15 oz.Suppose we take a random sample of 36 bottles filled by this machine.The probability that the mean of the sample is between 35.94 and 36.06 oz.is .

SCENARIO 7-4 According to a survey, only 15% of customers who visited the web site of a major retail store made a purchase.Random samples of size 50 are selected. -Referring to Scenario 7-4, what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the web site?

The amount of tea leaves in a can from a production line is normally distributed with $\mu = 110$ grams and $\sigma = 25$ grams.A sample of 25 cans is to be selected.What is the probability that thesample mean will be less than 100 grams?

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?

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, 80% of the samples will have less than% of minority students.

Which of the following is true about the sampling distribution of the sample mean?