Exam 7: Sampling Distributions

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, ____ % of the samples are likely to have between 35% and 40% who take advantage of online customer service.

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 7-7 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 standard error of the mean spending?

A sample that does not provide a good representation of the population from which it was collected is referred to as a(n) sample.

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 differs from the population mean by less 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, the requirements for using a normal distribution to approximate a binomial distribution is fulfilled for the random samples of Chinese consumers.

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. What Percentage of samples of 4 fish will have sample means between 3.0 and 4.0 pounds?

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 no more than $840?

The standard error of the population proportion will become larger

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 0.20 that the sample mean spending is no more than how much?

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 will be between 39 and 48 minutes?

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 __________.

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, 80% of the samples will have less than ______% of minority students.

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.

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

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?

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, the population mean of all the sample proportions 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 China will have less than 35% of consumers who will spend more on holiday shopping?

The standard deviation of the sampling distribution of a sample proportion is $\sqrt { \frac { \pi ( 1 - \pi ) } { n } } \text { where } \pi$ is the population proportion.

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 25 fish yields a mean of 3.6 pounds, what is the Z-score for this observation?