BUS Stats UNIT 3

The sample proportion is: A. an estimator of the population proportion B. an unbiased estimator of p C. a consistent estimator of p D. all of the above

All of the above

The relationship between a parameter and its corresponding statistic can be described as which of the following? 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. E. None of the above.

All of the above.

The mean of the sampling distribution of the sample mean is: A. always equal to the sample mean B. sometimes equal to the population mean. C. always equal to the population mean. D. always equal to the sampling procedure.

Always equal to the population mean.

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. approximately normal B. skewed C. Bi-modal

Approximately normal

The Central Limit Theorem states that when the sample size is sufficiently large, the sampling distribution of the proportion (namely, the distribution of the proportions, p̂ s, of all samples) will be ______________with its mean centered at ________________and its standard deviation equal to _________. A. Approximately normal; p; pq/n B. Approximately normal; p;pq/n in square root C. Approximately normal; μ; σ/n D. Approximately normal; p; 2/n E. Any of the above, depending F. None of the above.

Approximately normal; p; pq/n in square root

The mean of the sampling distribution of p̂ s is always equal to A. μ B. p C. p̂

p

The power of the test is A. α B. β C. (α + β ) D. (1 - α ) E. (1 - β )

(1 - β )

In a sample of 500 items produced on a machine, 7% are found to be defective. The 95% confidence interval for the proportion of defective items in all items produced by the machine is: A. 0.061 to 0.079 B. 0.057 to 0.083 C. 0.048 to 0.092 D. 0.032 to 0.108

0.048 to 0.092

A sample of 1000 families selected from a large city showed that 18% of them make $100,000 or more per year. The 99% confidence interval for the proportion of all families living in this city who make $100,000 or more per year is: A. 0.167 to 0.193 B. 0.171 to 0.189 C. 0.158 to 0.202 D. 0.149 to 0.211

0.149 to 0.211

A researcher wants to make a 99% confidence interval for the population mean. She wants the maximum error of estimate to be within 4.8 of the population mean. The population standard deviation is known to be 18.65. The sample size that will yield a maximum error of estimate within 4.8 of the population means is: A. 183 B. 101 C. 54 D. 155

101

A new manufacturing process is implemented. The quality control division has no historic estimate for p. How large a sample should be taken to be 95% confident that the sample proportion is within 0.02 of the population proportion? A. 2401 B. 1500 C. 1100 D. 349

2401

A researcher wants to make a 95% confidence interval for the population mean. She wants the maximum error of estimate to be within 2.5 of the population mean. The population standard deviation is known to be 10.50. The sample size that will yield a maximum error of estimate within 2.5 of the population mean is: A. 68 B. 95 C. 36 D. 78

68

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

95 of the intervals are expected to include μ.

The sign in the alternative hypothesis in a left- tailed test is always A. = B. ≠ C. > D. <

<

The sign in the alternative hypothesis in a right-tailed test is always A. = B. ≠ C. > D. <

>

A Type II error is made when A. a null hypothesis is not rejected when it is false. B. a null hypothesis is rejected when it is true. C. an alternative hypothesis is rejected when it is true.

A null hypothesis is not rejected when it is false.

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.

A null hypothesis is rejected when it is actually true.

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

A sample statistic

The null hypothesis is a claim: A. about a population parameter that is assumed to be false until it is declared true. B. about a population parameter that is assumed to be true until it is declared false. C. about a sample statistic that is assumed to be false until it is declared true. D. about a sample statistic that is assumed to be true until it is declared false.

About a population parameter that is assumed to be true until it is declared false.

The alternative hypothesis is a claim: A. about a population parameter that is assumed to be true until it is declared false. B. about a population parameter that will be true if the null hypothesis is false. C. about a sample statistic that will be true if the null hypothesis is false. D. about a sample statistic that is assumed to be false until it is declared true.

About a population parameter that will be true if the null hypothesis is false.

The sample mean is: A. an estimator of the population mean B. an unbiased estimator of μ C. a consistent estimator of μ D. all of the above

All of the above

The Central Limit Theorem states that regardless of the shape of the population distribution, the distribution of the samples' means will be _____________, provided the samples we take are _________. A. skewed; sufficiently large. B. approximately normal; sufficiently large. C. approximately normal; sufficiently small. D. none of the above.

Approximately normal; sufficiently large.

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

Becomes wider

The significance level, denoted by α , is the probability of A. committing a Type I error B. committing a Type II error C. neither A nor B D. could be both A and B

Committing a Type I error

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

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.

Decrease

When n increases, the standard error of the mean (namely, the standard deviation of the distribution of all the samples' means) A. increases B. decreases C. remains the same D. any of the above

Decreases

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

Decreases

In a two-tailed test of hypothesis, the two critical points: A. divide the area under the sampling distribution of a sample statistic into two rejection and one nonrejection regions. B. divide the area under the sampling distribution of a sample statistic into one rejection and two nonrejection regions.

Divide the area under the sampling distribution

In a one-tailed test of hypothesis, the critical point is a point that: A. divides the area under the sampling distribution of a sample statistic into one rejection and one nonrejection region. B. divides the area under the sampling distribution of a sample statistic into one rejection and two nonrejection regions.

Divides the area under the sampling distribution of a sample statistic into one rejection and one nonrejection region.

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

False

The standard error of the mean (namely, the standard deviation of the distribution of the samples' means) A. Measures the amount of variation in the sampling distribution. B. Measures the amount of dispersion of the population. C. Measures the amount of variability in the mean of the population. D. Measures the variation in a particular sample. E. None of the above.

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

More clustered

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

More likely

In a population of 9,500 TV sets, 75% are defective. In a sample of 400 sets selected from this population, 78% are found to be defective. How many TV sets in the population and sample, respectively, are defective?

Population: 7125 Sample: 312

The value of β gives the A. probability of committing a Type I error. B. probability of committing a Type II error. C. neither A nor B. D. could be both A or B.

Probability of committing a Type II error.

The standard error of the mean (namely, the standard deviation of the distribution of all samples' means) 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

Smaller than

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.

The difference between the value of a sample statistic and the value of the

Given the sample size, the standard error of the mean (namely, the standard deviation of the distribution of all the samples' means) 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 do with each other

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

The probability of rejecting a correct null hypothesis is __________________________________ which is represented by the symbol ________. A. the level of significance of a test; α B. the level of significance of a test; β C. the acceptance region; α D. the refection region; β

The level of significance of a test; α

The mean of the sampling distribution of the sample mean is: A. the mean of the means of all possible samples of the same size taken from the population. B. the mean of the frequency distribution of the population. C. the mean of the means of all frequency distributions. D. the mean of one sample.

The mean of the means of all possible samples of the same size taken from the population.

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

True

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

True

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

True

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

Two rejection regions

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 error; Type II error C. Type II error; Type I error D. z-score; α E. all of the above, depending F. none of the above

Type I error; Type II error

Consider a large population with p = 0.65. Find the mean and the standard deviation of the sampling distribution of the proportion when a. n = 100 b. n = 900

a.) 0.65 and about 0.048 b.) 0.65 and about 0.016

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

both np 5 >/ and nq >/ 5

The sampling distribution of the proportion (namely, the distribution of the proportion, p̂ s, of all samples) is approximately normal when A. both npq > 5 and nq > 5 B. both npq < 5 and nq < 5 C. np but nq < 5 D. both np < 5 and nq < 5 E. both npand nq F. n is 30 or more

both npand nq

How does the value of σ x̅ change as the sample size increases?

decrease

How does the value of σp̂ change as the sample size increases?

decrease

The standard deviation of the sampling distribution of the sample mean decreases when A. x increases B. n increases C. n decreases

n increases

The mean of the sampling distribution of x̅ is always equal to A. μ B. p C. x̅

μ

The standard deviation of the sampling distribution of the sample mean for a sample size of n drawn from a population with a mean of μ and a standard deviation of σ is: A. σ/n B. σ/2n C. σ/ square root n D. σ/n2

σ/ square root n

The sign in the alternative hypothesis in a two- tailed test is always A. = B. ≠ C. > D. <

≠