Exam 7: Sampling Distributions

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 standard deviation of the sampling distribution of the sample mean is ________ minutes.

TABLE 7-5 According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random sample sizes of 200 are selected from the country's population. -Referring to Table 7-5,among all the random sample sizes of 200,________% will have less than 20% who have high-speed access to the Internet.

True or False: If the population distribution is unknown,in most cases the sampling distribution of the mean can be approximated by the normal distribution if the samples contain at least 30 observations.

True or False: 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 has a standard error of 0.15.

TABLE 7-5 According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random sample sizes of 200 are selected from the country's population. -Referring to Table 7-5,among all the random sample sizes of 200,90% will have more than ________% who have high-speed access to the Internet.

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.So,95% of all sample means will be greater than how many grams?

TABLE 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 in order to estimate the mean study time for the population of all students. -Referring to Table 7-1,what is the probability that the sample mean differs from the population mean by less than 2 hours?

True or False: 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 has a mean of 36 oz.

TABLE 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 Table 7-2,what is the probability that the sample mean selling price was more than $110,000?

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

TABLE 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 Table 7-3,the probability is 0.15 that the sample mean lifetime is more than how many hours?

TABLE 7-4 According to a survey,only 15% of customers who visited the website of a major retail store made a purchase.Random sample sizes of 50 are selected. -Referring to Table 7-4,the mean of all the sample proportions of customers who will make a purchase after visiting the website is ________.

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams.A sample of 25 cans is to be selected.So,the middle 70% of all sample means will fall between what two values?

True or False: 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.

TABLE 7-5 According to an article,19% of the entire population in a developing country has high-speed access to the Internet.Random sample sizes of 200 are selected from the country's population. -Referring to Table 7-5,among all the random sample sizes of 200,________% will have more than 30% who have high-speed access to the Internet.

Sampling distributions describe the distribution of

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?

True or False: Suppose μ = 50 and σ = 10 for a population.In a sample where n = 100 is randomly taken,90% of all possible sample means will fall between 49 and 51.

The Central Limit Theorem is important in statistics because

True or False: The fact that the sample means are less variable than the population data can be observed from the standard error of the mean.