Exam 7: Sampling and Sampling Distributions

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.

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

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.

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

Measurement error will become an ethical issue when the findings are presented without reference to sample size and margin of error.

Which of the following is not a reason for selecting a sample?

The amount of tea leaves in a can from a particular production line is normally distributed with μ = 110 grams and σ = 25 grams. A sample of 25 cans is to be selected. What is the probability that the sample mean will be greater than 100 grams?

The Dean of Students mailed a survey to a total of 400 students. The sample included 100 students randomly selected from each of the freshman, sophomore, junior, and senior classes on campus last term. What sampling method was used?

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?

Major league baseball salaries averaged $3.26 million with a standard deviation of $1.2 million in a recent year. Suppose a sample of 100 major league players was taken. Find the approximate probability that the mean salary of the 100 players was no more than $3.0 million.

A sampling distribution is defined as the probability distribution of possible sample sizes that can be observed from a given population.

TABLE 7-7 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 Table 7-7, the standard error of all possible sample proportions is ________.

TABLE 7-7 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 Table 7-7, the population mean of all possible sample proportions is ________.

TABLE 7-6 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 Table 7-6, among all the random samples of size 200, ________ % will have between 9% and 29% who have high-speed access to the Internet.

TABLE 7-5 According to a survey, only 15% of customers who visited the website of a major retail store made a purchase. Random samples of size 50 are selected. -Referring to Table 7-5, the standard deviation of all the sample proportions of customers who will make a purchase after visiting the website is ________.

A sample is always a good representation of the target population.

Which of the following types of samples can you use if you want to make valid statistical inferences from a sample to a population?

The standard error of the mean

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.

________ results from the failure to collect data on all subjects in the sample.