Exam 7: Sampling Distributions

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, what proportion of the samples from U.S. will have between 30% and 50% of consumers who will spend more on holiday shopping?

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 in order 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 exceeds the population mean by more than 2 hours?

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, 90% of the samples from China will have less than what percentage of consumers who will spend more on holiday shopping?

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, 90% of the samples from U.S. will have more than what percentage of consumers who will spend more on holiday shopping?

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, the standard deviation of all the sample proportions of Canadian consumers who will spend more on holiday shopping is ________.

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, 90% of the samples from Canada will have less than what percentage of consumers who will spend more on holiday shopping?

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country have 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.

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 more than what percentage of customers who will make a purchase after visiting the web site?

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 __________.

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, what proportion of the samples from U.S. will have less than 35% of consumers who will spend more on holiday shopping?

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 mean of the sampling distribution of a sample proportion is the population proportion,π.

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?

SCENARIO 7-7 A recent survey revealed that American's Christmas spending averaged $830. Use this as the population mean American's Christmas spending. Suppose American's Christmas spending is normally distributed with a standard deviation of $220. Random sample of size 100 are selected from the population of American consumers. -Referring to Scenario 7-7, the middle 50% of the sample mean spending will be bounded by what two values?

Sales prices of baseball cards from the 1960s are known to possess a right skewed distribution with a mean sale price of $5.25 and a standard deviation of $2.80. Suppose a random sample of 100 cards from the 1960s is selected. Describe the sampling distribution for the sample mean sale Price of the selected cards.

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.

A study at a college in the west coast reveals that, historically, 45% of the students are minority students. If a random sample of size 75 is selected, the probability is _______ that more than half of the students in the sample will be minority students.

SCENARIO 7-5 According to an article, 19% of the entire population in a developing country have 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 between 9% and 29% who have high-speed access to the Internet.

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?

SCENARIO 7-8 A consulting firm that surveyed consumers' holiday shopping behavior found that the percentage of consumers from the U.S., Canada, and China who said that they planned to spend more on holiday shopping were 40%, 34% and 73%, respectively. Treat these results as representations of the populations. Random samples of size 150 are selected from each of the three countries. -Referring to Scenario 7-8, what proportion of the samples from Canada will have between 30% and 50% of consumers who will spend more on holiday shopping?