Exam 7: Sampling Distributions

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,without doing the calculations,state in which of the following ranges the sample mean selling price is most likely to lie.

For a sample size of 16,the sampling distribution of the mean will be approximately normally distributed

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 greater than 88 minutes is ________.

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,what is the probability that the sample mean lifetime is more than 1,550 hours?

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

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 exceeds 36.01 oz.is ________.

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.95% of all sample means will fall between what two values?

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 probability that the sample mean will be between 77 and 89 minutes is ________.

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

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,what proportion of the samples will have less than 15% of customers who will make a purchase after visiting the website?

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

True or False: Suppose μ = 50 and σ = 10 for a population.In a sample where n = 100 is randomly taken,95% of all possible sample means will fall between 48.04 and 51.96.

True or False: If the population distribution is symmetric,the sampling distribution of the mean can be approximated by the normal distribution if the samples contain 15 observations.

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

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. -A study at a college in the west coast reveals that,historically,45% of the students are minority students.If random sample sizes of 75 are selected,80% of the samples will have less than ________% of minority students.

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 ________.

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 middle 95% of the sample means based on sample sizes of 36 will be between ________ and ________.

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.90% of the sample means will be greater than what value?

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 0.20 that the sample mean lifetime differs from the population mean lifetime by at least how many hours?