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Exam 7: Sampling Distributions

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Question 1

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According to the Central Limit Theorem, any sampling distribution of is considered normal provided .

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B) False

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Question 2

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Completely describe the distribution of the sample proportion for samples of size n = 500 from a population with p = 0.4. Is the sampling distribution of the sample proportion approximately normal? ______________ What is the mean? ______________ What is the standard deviation? ______________

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Question 3

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Which of the following is not a correct statement about the systematic random sample?

The expression SE ( ) represents the standard error sampling distribution of the sample proportion, .

A TV pollster believed that 70% of all TV households would be tuned in to Game 6 of the 1997 NBA Championship series between the Chicago Bulls and the Utah Jazz. A random sample of 500 TV households is selected. Is the sampling distribution of the sample proportion approximately normal? ______________ What is the mean? ______________ What is the standard deviation? ______________ Find the probability that the sample proportion on will be between 0.65 and 0.75. ______________

The standard error of the sampling distribution of the sample proportion when n = 100 and p = 0.15 is 0.001275.

The amount of money spent on food per week by an American family is known to have a mean of $92 and a standard deviation of $9. Suppose a random sample of 81 families is taken and their sample mean food expenditure is calculated. Find the mean of the sampling distribution of . ______________ Find the standard deviation. ______________ Find the probability that the sample mean does not exceed $90.40. ______________

Consider a large population with a mean of 150 and a standard deviation of 27. A random sample of size 36 is taken from this population. The standard error of the sampling distribution of sample mean is equal to:

The total daily sales, x, in the deli section of Carter, a local market in Big Rapids, is the sum of the sales generated by a fixed number of customers who make purchases on a given day. Is the sampling distribution of the total daily sales approximately normal? ______________ For this particular market, the average sale per customer in the deli section is $10.50 with = $2.50. If 30 customers make deli purchases on a given day, give the mean and standard deviation of the probability distribution of the total sales, x. What is the mean? ______________ What is the standard deviation? ______________

Let be 1 if a success occurs and 0 otherwise. Let i.e., x is the count of the number of successes in n trials. If a random sample is taken from a population which contains only zeros and ones, the sample mean is an estimate of the actual proportion of ones in the population.

One of the most common sources of random cause variation is the people who are working in the process.

Standard error of the sample proportion is another term for the variance of the sampling distribution of the sample proportion .

Process control charts, such as the and p-charts, are used to provide signals to indicate when the output of a process is out of control.

Random variation in a process can be eliminated.

Graduate students applying for entrance to many universities must take a Miller Analogies Test. It is known the test scores have a mean of 75 and a variance of 16. This year, one hundred students applied for entrance into graduate school in physics. Find the mean of the sampling distribution of . ______________ Find the standard deviation. ______________ Find the probability that the average score of this group of students is higher than 76. ______________

If is the mean of a simple random sample taken from a large population and if the N population values are normally distributed, the sampling distribution of is also normally distributed, regardless of sample size, n.

Which of the following correctly describes a sample?

The stratified random sample is a subset of a frame, or of an associated population, chosen by randomly selecting one of the first k elements and then including every kth element thereafter until the desired sample size has been reached.

If a sample of n elements is selected from a population of N elements using a sampling plan in which each of the possible samples has the same chance of being selected, then the sampling is said to be random and the resulting sample is a simple random sample.

The usable lifetime of a particular type of battery is normally distributed with a mean of 1,100 days and a standard deviation of 80 days. The manufacturer randomly selects 400 batteries of this type and ships them to K-Mart. What is the mean of the sampling distribution of ? ______________ What is the standard deviation? ______________ What is the probability the average usable lifetime of these 400 batteries is between 1,097 and 1,104 days? ______________