STATS EXAM 3 - Ch 7 questions (7.1-7.6)

A sample of 400 observations will be taken from an infinite population. The population proportion equals 0.8. The probability that the sample proportion will be greater than 0.83 is 0.0668. 0.4332. 0.9332. 0.5668.

0.0668

How many simple random samples of size 5 can be selected from a population of size 8? 336 40 68 56

56

A random sample of 150 people was taken from a very large population. Ninety of the people in the sample were female. The standard error of the proportion is 0.1600. 0.0016. 0.2400. 0.0400.

0.0400.

A sample of 66 observations will be taken from an infinite population. The population proportion equals 0.12. The probability that the sample proportion will be less than 0.1768 is 0.42. 0.06. 0.08. 0.92.

0.92

A simple random sample of 64 observations was taken from a large population. The sample mean and standard deviation were determined to be 320 and 120 respectively. The standard error of the mean is 5. 1.875. 40. 15.

15.

A random sample of 12 four-year-old red pine trees was selected and the diameter (in inches) of each tree's main stem was measured. The resulting observations are as follows: 11.3 10.7 12.4 15.2 10.2 12.1 16.2 10.5 11.4 11.0 10.7 12.0 Find the point estimate that can be used to estimate the true population mean. Answers: = 11.97 = 1.73 s = 3.24 s = 14.02

= 11.97

Which of the following is(are) true? i. The mean of a population depends on the particular sample chosen. ii. The standard deviations of two different samples from the same population may be the same. iii. Statistical inferences can be used to draw conclusions about the populations based on sample data.

II and III

The Central Limit Theorem is important in Statistics because It enables reasonably accurate probabilities to be determined for events involving the sample average when the sample size is large regardless of the distribution of the variable. it tells us that large samples do not need to be selected. It guarantees that when it applies, the samples that are drawn are always randomly selected. It tells us that if several samples have produced sample averages, which seem to be different than expected, the next sample average will likely be close to its expected value.

It enables reasonably accurate probabilities to be determined for events involving the sample average when the sample size is large regardless of the distribution of the variable.

Which of the following statements regarding the sampling distribution of sample means is incorrect? The standard deviation of the sampling distribution is the standard deviation of the population. The sampling distribution is approximately normal when the population is normal or the sample size is sufficiently large. The mean of the sampling distribution is the mean of the population. The sampling distribution is found by taking repeated samples of the same size from the population of interest and computing the mean of each sample.

The standard deviation of the sampling distribution is the standard deviation of the population.

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. In this problem, the value 0.22 ounces is the standard error of the mean. a parameter. a statistic. the average content of colognes in the long run.

a parameter.

The medical director of a company looks at the medical records of all 50 employees and finds that the mean systolic blood pressure for these employees is 126.07. The value of 126.07 is a statistic. a sample. a population. a parameter.

a parameter.

The Central Limit Theorem states that if n is large, then the sampling distribution of the sample mean can be approximated closely by a normal curve. if n is large, then the distribution of the sample can be approximated closely by a normal curve. if n is large and if the population is normal, then the variance of the sample mean must be small. if n is large and if the population is normal, then the sampling distribution of the sample mean can be approximated closely by a normal curve.

a. if n is large, then the sampling distribution of the sample mean can be approximated closely by a normal curve.

Random samples of size 100 are taken from an infinite population whose population proportion is 0.2. The mean and standard deviation of the sample proportion are 20 and 0.04. 0.2 and 0.04. 0.2 and 0.2. 20 and 0.2.

b. 0.2 and 0.04.

A simple random sample from an infinite population is a sample selected such that a. each element has a probability of at least 0.5 of being selected. b. each element is selected independently and is selected from the same population. c. each element has a 0.5 probability of being selected. d. the probability of being selected changes.

b. each element is selected independently and is selected from the same population.

A simple random sample of size n from a finite population of size N is a sample selected such that each possible sample of size a. n has a probability of 0.1 of being selected. b. N has the same probability of being selected. c. n has a probability of 0.5 of being selected. d. n has the same probability of being selected.

d. n has the same probability of being selected.

It is impossible to construct a sampling frame for a(n) target population. finite population. infinite population. defined population.

infinite population.

As a rule of thumb, the sampling distribution of the sample proportions can be approximated by a normal probability distribution when np ≥ 5. n(1 - p) ≥ 5 and np ≥ 5. n ≥ 30 and n(1 - p) = 5. None of these alternatives is correct.

n(1 - p) ≥ 5 and np ≥ 5.

A sample of 92 observations is taken from an infinite population. The sampling distribution of x-bar is approximately normal because of the central limit theorem. normal because is always approximately normally distributed. normal because the sample size is small in comparison to the population size. None of these alternatives is correct.

normal because of the central limit theorem.

Parameters are the averages taken from a sample. numerical characteristics of a sample. numerical characteristics of a population. numerical characteristics of either a sample or a population.

numerical characteristics of a population.

Sample statistics, such as x-bar , s, or p-bar , that provide the point estimate of the population parameter are known as population parameters. point estimators. parameters. population statistics.

point estimators.

Sampling distribution of (p-bar) is the mean of the sample. probability distribution of the sample mean. probability distribution of the sample proportion. mean of the population.

probability distribution of the sample proportion.

Doubling the size of the sample will have no effect on the standard error of the mean. reduce the standard error of the mean. increase the standard error of the mean. double the standard error of the mean.

reduce the standard error of the mean.

In a recent Gallup Poll the decision was made to increase the size of its random sample of voters from 1500 people to about 4000 people. The purpose of this increase is to reduce the variability of the estimate. reduce the bias of the estimate. increase the standard error of the estimate. increase the confidence interval width for the parameter.

reduce the variability of the estimate.

Which of the following is a point estimator? s σ μ p

s

Which of the following is not a symbol for a parameter? s µ ρ σ

s

The value of the ___________ is used to estimate the value of the population parameter. population estimate population statistic sample parameter sample statistic

sample statistic

When drawing a sample from a population, the goal is for the sample to be smaller than the targeted population. sample to match the targeted population. sample to include some of the targeted population. sample to be more varied than the targeted population.

sample to match the targeted population.

The probability distribution of all possible values of the sample proportion (p -bar) is the same as , since it considers all possible values of the sample proportion (p-bar) probability density function of (p-bar) . sampling distribution of (x-bar). sampling distribution of (p-bar).

sampling distribution of (p-bar).

The distribution of values taken by a statistic in all possible samples of the same size from the same population is called a sampling distribution. sample. population. distribution of interest.

sampling distribution.

A statistic, calculated from a random representative sample, influences the value of the population parameter. is always equal to the value of the population parameter it estimates. is always based upon a sample size that is greater than the population size. should be an unbiased estimator of the population parameter.

should be an unbiased estimator of the population parameter.

As the sample size increases, the standard error of the mean decreases. standard deviation of the population decreases. population mean increases. standard error of the mean increases.

standard deviation of the population decreases.

As the sample size increases, the standard error of the mean decreases. standard deviation of the population decreases. population mean increases. standard error of the mean increases.

standard error of the mean decreases.

The standard deviation of a point estimator is called the point variability. standard deviation. standard error. variance of estimation.

standard error.

The standard deviation of a point estimator is called the point estimator. standard deviation. standard error. variance of estimation.

standard error.

The population we want to make inferences about is the target population. sampled population. frame. finite population.

target population.

A simple random sample of size n from an infinite population of size N is to be selected. Each possible sample should have a probability of 1/N of being selected. the same probability of being selected. a probability of 1/n of being selected. a probability of N/n of being selected.

the same probability of being selected.

The distribution of values taken by a statistic in all possible samples of the same size from the same population is the sampling distribution of the distribution. the sample. the population. the target population.

the sample

The sample statistic s is the point estimator of ρ. μ. σ. π.

σ.