Exam 7: Sampling Distributions

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 90% of the sample mean spending will be bounded by what two values?

The standard error of the mean for a sample of 100 is 30. In order to cut the standard error of the mean to 15, we would

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 mean of all the sample proportions of U.S. consumers who will spend more on holiday shopping 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. The probability that the sample mean will be between 77 and 89 minutes is __________.

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

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

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 Chinese consumers who will spend more on holiday shopping is ________.

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, what is the probability that the sample mean spending is less than $815 or more than $855?

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 proportion of the samples will have between 20% and 30% of customers who will make a purchase after visiting the web site?

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 it is assumed that the amount of gasoline purchased per car is symmetric, there is approximately a 68.26% chance that a random sample of 16 cars will have a sample mean between 14 and 16 gallons.

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 between 30% and 50% of the students in the sample will be minority students.

The amount of time it takes to complete an examination has a left skewed distribution with a mean of 65 minutes and a standard deviation of 8 minutes. If 64 students were randomly sampled, the probability that the sample mean of the sampled students exceeds 71 minutes is approximately 0.

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 probability is 0.15 that the sample mean spending is less than how much?

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a certain year in the past. Suppose a sample of 100 major league players was taken. Find the Approximate probability that the mean salary of the 100 players exceeded $3.5 million.

At a computer manufacturing company, the actual size of a particular type of computer chips is normally distributed with a mean of 1 centimeter and a standard deviation of 0.1 centimeter. A Random sample of 12 computer chips is taken. What is the standard error for the sample mean?

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 probability is 0.15 that the sample mean spending is more than how much?

To use the normal distribution to approximate the binomial distribution, we need ______ and ______ to be at least 5.

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

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 4 cars is selected, there is approximately a 68.26% chance that the sample mean will be between 13 and 17 gallons.

The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with mean of 3.2 pounds and standard deviation of 0.8 pound. If a sample of 16 fish is taken, what would the standard error of the mean weight equal?