Exam 7: Sampling Distributions

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?

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, 95% of the samples proportions symmetrically around the population proportion will have between _____% and _____% of the customers who take advantage of online customer service.

As the sample size increases, the effect of an extreme value on the sample mean becomes smaller.

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

Why is the Central Limit Theorem so important to the study of 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 probability is 0.20 that the sample mean spending is at least how much?

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

The Central Limit Theorem is considered powerful in statistics because it works for any population distribution provided the sample size is sufficiently large and the population mean and standard deviation are known.

As the size of the sample is increased, the standard deviation of the sampling distribution of the sample mean for a normally distributed population will stay the same.

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 standard error of the mean?

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 will be approximately normal only if the population sampled is normal.

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 64 fish yields a mean of 3.4 pounds, what is probability of obtaining a sample mean this large or Larger?

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. What was the Standard error for the sample mean salary?

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.

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.

μ The am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. What is the probabilityally distributed with that the sample mean will be between 100 and 120 grams?

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 standard error of all the sample proportions is ______.

μThe am = 110 gramount of tea leaves in a can froms and σ = 25 grams. A sam a particular production line is normple of 25 cans is to be selected. So, 95% of all samally distributed with ple means will be greater than how many grams?

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 less than 15% of customers who will make a purchase after visiting the web site?

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 more than what percentage of consumers who will spend more on holiday shopping?