Exam 7: Sampling Distributions

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 __________.

In inferential statistics, the standard error of the sample mean assesses the uncertainty or error of estimation.

Using the finite population correction (fpc)for sampling distributions of finite populations, the corrected standard error is larger giving more precise estimates.

The standard error of the mean is also known as the standard deviation of the sampling distribution of the sample mean.

The finite population correction is used when:

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken.The mean of the sampling distribution of the sample mean is __________ minutes.

As the sample size increases, the standard error of the mean increases.

A manufacturer of power tools claims that the mean amount of time required to assemble their top-of-the-line table saw is 80 minutes with a standard deviation of 40 minutes. Suppose a random sample of 64 purchasers of this table saw is taken.The probability that the sample mean will be less than 82 minutes is __________.

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.Suppose 100 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 these 100 flights.

The mean of the sampling distribution of a sample proportion is the population proportion,

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 is the probability that a random sample of 50 will have at least 30% of customers who will make a purchase after visiting the web site?

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, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the web site is ________.

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons, then 99.73% of all cars will purchase between 3 and 27 gallons.

The Central Limit Theorem ensures that the sampling distribution of the sample mean approaches a normal distribution as the sample size increases.

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, 95% of the samples will have more than ______% of minority students.

The amount of tea leaves in a can from a production line is normally distributed with grams and grams.A sample of 25 cans is to be selected.What is the probability that the sample mean will be greater than 100 grams?

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

If the amount of gasoline purchased per car at a large service station has a population mean of 15 gallons and a population standard deviation of 4 gallons and a random sample of 64 cars is selected, there is approximately a 95.44% chance that the sample mean will be between 14 and 16 gallons.

Suppose the ages of students in Statistics 101 follow a right skewed distribution with a mean of 23 years and a standard deviation of 3 years.If we randomly sampled 100 students, which of the following statements about the sampling distribution of the sample mean age is incorrect?

The mean score of all pro golfers for a course has a mean of 70 and a standard deviation of 3.0.Suppose 36 pro golfers played the course today.Find the probability that the mean score of the 36 pro golfers exceeded 71.