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Exam 7: Sampling and Sampling Distributions

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Question 1

Multiple Choice

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A probability distribution for all possible values of a sample statistic is known as a

A) sample statistic
B) parameter
C) simple random sample
D) sampling distribution

E) All of the above
F) A) and B)

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Question 2

Multiple Choice

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A simple random sample from a process (an infinite population) is a sample selected such that

A) each element selected comes from the same population
B) each element is selected independently
C) each element selected comes from the same population and each element is selected independently
D) the probability of being selected changes

E) B) and D)
F) C) and D)

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C

Question 3

Multiple Choice

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The standard deviation of is referred to as the

Consider a population of five families with the following data representing the number of pets in each family. a.There are ten possible samples of size 2 (sampling without replacement). List the 10 possible samples of size 2, and determine the mean of each sample. b.Determine the mean and the variance of the population. c.Using the ten sample mean values, compute the mean and the standard error of the mean.

A population has a mean of 80 and a standard deviation of 7. A sample of 49 observations will be taken. The probability that the mean from that sample will be larger than 82 is

All of the following are true about the standard error of the mean except

The population being studied is usually considered ______ if it involves an ongoing process that makes listing or counting every element in the population impossible.

When the population has a normal distribution, the sampling distribution of is normally distributed

Ten percent of the items produced by a machine are defective. A random sample of 100 items is selected and checked for defects. a.Determine the standard error of the proportion. b.What is the probability that the sample will contain more than 2.5% defective units? c.What is the probability that the sample will contain more than 13% defective units?

A population has a mean of 180 and a standard deviation of 24. A sample of 64 observations will be taken. The probability that the mean from that sample will be between 183 and 186 is

Roger Hall, who oversees six Ford dealerships, believes that the colors chosen by customers who special-order their cars best reflect most customers' true color preferences. For that reason, he has tabulated the color requests specified in a sample of 56 Mustang coupe special orders placed this year. The sample data are listed below. a. What is the point estimate of the proportion of all Mustang coupe special orders that specify a color preference of black? b. Describe the sampling distribution of , where is the proportion of Mustang coupe special orders that specify a color preference of black. Assume that the proportion of all Mustang coupe special orders having a color preference of black is .36. c. What is the probability that a simple random sample of 56 special orders will provide an estimate of the population proportion of special orders specifying the color black that is within plus or minus .05 of the actual population proportion, assuming p = .36? In other words, what is the probability that will be between .31 and .41?

A random sample of ten examination papers in a course that was given on a pass or fail basis showed the following scores. a.What is the point estimate for the mean of the population? b.What is the point estimate for the standard deviation of the population? c.What is the point estimate for the proportion of all students who passed the course?

Scores for a standardized test are normally distributed with a mean of 1200 and a standard deviation of 60. A sample of 36 scores is selected. a.What is the probability that the sample mean will be larger than 1224? b.What is the probability that the sample mean will be less than 1230? c.What is the probability that the sample mean will be between 1200 and 1214? d.What is the probability that the sample mean will be greater than 1200? e.What is the probability that the sample mean will be larger than 73.46?

The basis for using a normal probability distribution to approximate the sampling distribution of is

The number of random samples (without replacement) of size 3 that can be drawn from a population of size 5 is

A population of 1,000 students spends an average of $10.50 a day on dinner. The standard deviation of the expenditure is $3. A simple random sample of 64 students is taken. a.What are the expected value, standard deviation, and shape of the sampling distribution of the sample mean? b.What is the probability that these 64 students will spend a combined total of more than $715.21? c.What is the probability that these 64 students will spend a combined total between $703.59 and $728.45?

As the sample size increases, the

The sample mean is the point estimator of

Exhibit 7-4 A random sample of 121 bottles of cologne showed an average content of 4 ounces. It is known that the standard deviation of the contents (i.e., of the population) is 0.22 ounces. -Refer to Exhibit 7-4. In this problem the 0.22 is

The sampling distribution of the sample mean