Exam 7: Sampling Distributions

A study at a college in the west coast reveals that, historically, 45% of the students are minority students.The expected percentage of minority students in their next group of freshmen is.

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, among all the random samples of size 200, % will have more than 30% who have high-speed access to the Internet.

The standard error of the mean

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

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, the population mean of all possible sample proportions is .

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

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 is between 45 and 52 minutes?

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.

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 less than 2 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 less than 36.03 is .

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.So, the middle 95% of the sample means based on samples of size 64 will be between and .

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 requirements for using a normal distribution to approximate a binomial distribution is fulfilled.

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

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

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$113,000 and $117,000?

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.So, the middle95% of the sample means based on samples of size 36 will be between and.

Suppose a sample of n = 50 items is selected from a population of manufactured products and the weight, X, of each item is recorded.Prior experience has shown that the weight has a probabilitydistribution with $\mu$ = 6 ounces and $\sigma$ = 2.5 ounces.Which of the following is true about thesampling distribution of the sample mean if a sample of size 15 is selected?

SCENARIO 7-3 The lifetimes of a certain brand of light bulbs are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.A random sample of 64 of these light bulbs is taken. -Referring to Scenario 7-3, the probability is 0.15 that the sample mean lifetime is more than how many hours?

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

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.