Business Statistics Exam III

The sample size needed to estimate a parameter is A. larger the larger the confidence coefficient is B. larger the larger the variance is C. larger the more precisely you want to be able to estimate the parameter D. all of the above E. none of the above

D

With a fixed sample size, as Type I error increases, Type II error A. approaches 150% B. approaches 1. C. also increases D. decreases E. none of the above

D

The relationship between a parameter and its corresponding statistic can be described as? A. The statistic deals only with the sample, while the parameter deals with the population. B. The statistic is often a good estimator of the parameter. C. If the estimator is consistent, as the sample size becomes large, the value of the statistic approaches the value of the parameter. D. All of the above

D. All of the above

When is an estimator unbiased? Is the sample mean an unbiased estimator of mu? Explain why or why not

When the mean is equal to the parameter. Yes, because it is equal to the population mean.

How does the values of x(bar) change as the sample size increases?

It decreases

A sampling error is A. the difference between the value of a sample statistic based on a random sample and the value of the corresponding population parameter B. the error made while collecting, recording, and tabulating data C. the error that occurs because the sample is too small

A

A two-tailed test is a test with A. two rejection regions B. two nonrejection regions C. two test statistics

A

The critical value enables us to identify the rejection region in hypothesis testing A. true B. false

A

The further away the mean of our sample is from the hypothesized population mean; the _____ we are to reject the null hypothesis A. More likely B. Less likely

A

The mean of sampling distribution of X bar is always equal to? A. M B. p C. x(bar)

A

The probability of rejecting a correct null hypothesis is ____ which is represented by the symbol ________ A. The level of significance of a test; alpha B. Level of significance of a test; beta C. The acceptance region; alpha D. The rejection region; beta

A

The sampling distribution of p(hat) is normal if A. both np>5 and nq>5 B. both np<5 and nq<5 C. np>5 and nq<5

A

The signigican level, denoted by alpha, is the probability of A. committing a type I error B. committing a type II error C. neither a or b D. could be both

A

The sign in the alternative hypothesis in a right-tailed test could be A. = B. not equal C. > D. <

A & C

The sign in the alternative hypothesis in a left-tailed test could be A.= B. not equal C. > D. <

A & D

When the sample size is equal to or more than 30, the distribution of the samples' means will be _____ even though the population distribution may be extremely skewed A. Approx. Normal B. Skewed C. Bi-Modal

A. Approx. Normal

The standard error of the mean (standard deviation of the samples mean) A. Measures the amount of variation in the sampling distribution B. Measures the amount of dispersion in the population C. Measures the amount of variability in the mean of the population D. Measures the variation in a particular sample

A. Measures the amount of variation in the sampling distribution

As n increases, the sample means will become ______ around the population mean A. More clustered B. Less clustered C. Bi-Modal

A. More clustered

An estimator is said to be unbiased if the expected value of the statistic is equal to the value of the corresponding parameter A. True B. False

A. True

The wider the confidence interval is, the less precise is our estimate of the parameter A. True B. False

A. True

Given the sample size, the standard error of the mean will be larger A. the larger the standard deviation of the population from which the samples are taken is B. the smaller the standard deviation of the population from which the samples are taken is. C. the two have nothing to with each other

A. the larger the standard deviation of the population from which the samples are taken is

A sampling distribution is the probability distribution of A. A population parameter B. A sample statistic C. Any random variable

B

A type I error is made when A. a null hypothesis is not rejected when it is actually false B. a null hypothesis is rejected when it is actually true C. an alternative hypothesis is rejected when it is actually true

B

Nonsampling errors are the errors A. that occur because the sample size is too large in relation to the population size B. made while collecting, recording, and tabulating data C. that occur because an untrained person conducts a survery

B

How does the value of p(hat) change as the sample size increases?

It decreases

The Central Limit Theorem states that when the sample size is sufficiently large, the sampling distribution of a proportion will be __________ with its mean centered at _______ and its standard deviation equal to _______________ A. approx normal; p;pq/n B. approx normal; p; square root of pq/n C. approx normal; m; o/n D. approx normal; p; o^2/n E. Any of them F. None

B

The error of rejecting a true null hypothesis is called ____ and the error of not rejecting a false null hypothesis is called ____ A. Confidence coefficient; standard error B. Type I; Type II error C. Type II error, Type I error D. Z-score; alpha E. All of the above F. None of these

B

The formula for the standard error of the proportion used in hypothesis testing is the same as the used in interval estimation A. true B. false

B

The mean of the sampling distribution of p(hat) is always equal to A. M B. P C. P(hat)

B

The sampling error is defined as A. an error that occurs during collection, recording, and tabulation of data B. the difference between the value of a sample statistic and the value of the corresponding population parameter C. an error that occurs when a sample of less than 30 elements is drawn D. an error that occurs when a sample of more than 30 elements is drawn

B

The sign in the alternative hypothesis in a two-tailed test is always A. = B. not equal C. > D.<

B

The value of Beta gives the A. probability of committing a type I error B. probability of committing a type II error. C. neither C. could be both

B

The Central Limit Theorem states that regardless of the shape of the population distribution, the distribution of the samples' mean will be _____ provided that the samples we take are________. A. Skewed; larger B. Approx. Normal; larger C. Approx Normal; small D. None

B. Approx. Normal; Larger

As the confidence coefficient (CC) increases, the confidence interval A. becomes narrower B. becomes wider C. remains the same

B. Becomes wider

If an estimator tends to approach the value of the population parameter as the sample size increases that estimator is said to be A. Unnbiased B. Consistent C. Consistently unbiased D. Point Estimator E. Interval Estimator

B. Consistent

As sample size (n) increases, the probability that the mean of a sample will be very far away from the mean of the population will: A. Increase B. Decrease C. Not change D. Any of the above, depending

B. Decrease

When n increases, the standard error of the mean A. Increases B. Decreases C. Remains the same D. Any of the above

B. Decreases

The sample mean is an inconsistent estimator of the population mean A. True B. False

B. False

The standard error of the mean is ________ the standard deviation of the population from which the samples are taken A. Smaller than B. Larger than C. Equal to D. Not at all related to

B. Larger than

A 95% confidence interval for M can be interpreted to mean that if we take 100 samples of the same size and construct 100 such confidence interval for M then A. 95 of the intervals are expected to not include M B. 95 of the intervals are expected to include x(bar) C. 95 of the intervals are expected to include M

C

The probability distribution of a sample statistic is called: A. the frequency distribution of that statistic B. the binomial distribution of that statistic C. the sampling distribution of that statistic D. the Poisson of that statistic

C

The sampling distribution is the probability distribution of A. a sample B. a parameter C. a sample statistic

C

What is the difference between the critical z and the observed z?

Critical value is the value that would have been obtained if chance alone contributed to the outcome at the chosen level of significance. Observed value is the value you obtain from the test statistic to be compared with the critical value.

The power of a test is A. alpha B. Beta C. (alpha + beta) D. (1-alpha) E. (1-beta)

E

The sampling distribution of the proportion is approx normal when A. both npq> and nq>5 B. both npq<5 and nq<5 C. np> 5 but nq<5 D. both np < 5 and nq<5 E. both np >5 and nq>5 F. n is 30 or more

E

Type I error plus Type II error A. always equals 1 B. can never equal 1 C. always equals 0 D. must always be equal to 0.5 E. must always be greater than 1.0 F. none of the above

F

What does the level of significance represent in a test of hypothesis?

P-value

Explain the central limit theorem.

States that given a sufficiently large sample size from a population with a finite level of variance, the mean of all samples from the same population will be approximately equal to the mean of the population.

By rejecting the null hypothesis, are you stating the alternative hypothesis is true?

Yes