Business Statistics exam 3

stratified random sampling

A form of probability sampling; a random sampling technique in which the researcher identifies particular demographic categories of interest and then randomly selects individuals within each category.

reject the null hypothesis if the p-value is less than a, do not reject the null if p is greater than a A. true B. false

A. true

a type 2 error

we do not reject the null hypothesis when the null hypothesis is actually false

A type 1 error

we reject the null hypothesis when the null hypothesis is actually true. Also called a false positive

Which of the following is considered an estimate? A. u = 12 B. x (lower case) = 20 C. a = 3.2 D. a(squared) = 10

B. x (lower case) = 20

Hypothesized population means can assume any value A. true B. false

A. true

Sample

a subset of the population

nonresponse bias

refers to a systematic difference in preferences between respondents and non-respondents to a survey or poll

selection bias

refers to a systematic underrepresentation of certain groups from consideration for the sample

Using the central limit theorem applied to the sampling distribution of the sample proportion, what conditions must be met?

np≥5 and n(1−p)≥5

Which of the following meets the requirements of a cluster sample? A. A population can be divided into 50 city blocks, The sample will include one hundred people who volunteer for the sample from any city block. B. A population can be divided into 50 city blocks. The sample will include one hundred people chosen at random, without regard to the city block where they live. C. A population can be divided into 50 city blocks. The sample will include all residents from two randomly chosen city blocks. D. A population can be divided into 50 city blocks. The sample will include two people chosen at random from each city block.

C. A population can be divided into 50 city blocks. The sample will include all residents from two randomly chosen city blocks.

What is the purpose of calculating a confidence interval? A. To provide a range of values that has a certain large probability of containing the sample statistic of interest B. To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest C. To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest D. To provide a range of values that has a certain large probability of containing the population parameter of interest.

C. To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest

The null hypothesis states the status quo, the alternative hypothesis contests it. they are mutually exclusive A. true B. false

A. true

When specifying the competing hypotheses it is important to

1. identify the relevant population parameter 2. determine whether a one or two tailed test is appropriate 3. include some form of the equality sign in the null hypothesis and use the alternative hypothesis to establish a claim

Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. What supports this when selecting sample sizes? A larger sample size reduces the margin of error The t distribution consists of

A larger sample size reduces the margin of error The t distribution consists of

Two random samples are considered independent if the process that generates one sample is completely separate from the process that generates the other sample A. true B. false

A. true

cluster sampling

A probability sampling technique in which clusters of participants within the population of interest are selected at random, followed by data collection from all individuals in each cluster. Sample every observation in those randomly selected clusters.

competing hypotheses should state the value of parameter being tested, with opposing arguments in each hypothesis A. true B. false

A. true

To test if the mean IQ of employees in an organization is greater than 100, a sample of 30 employees is taken and the value of the test statistic is computed as t29 = 2.42 If we choose a 5% significance level, we _____________ .A) reject the null hypothesis and conclude that the mean IQ is greater than 100 B) reject the null hypothesis and conclude that the mean IQ is not greater than 100 C) do not reject the null hypothesis and conclude that the mean IQ is greater than 100 D) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100

A) reject the null hypothesis and conclude that the mean IQ is greater than 100

Which of the following is the necessary condition for creating confidence intervals for the population mean? A. Normality of the estimator B. Normality of the population C. Known population parameter D. Known standard deviation of the estimator

A. Normality of the estimator

A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, Ho:μ ≥ 6 and HA:μ < 6, μ stand for _____________. A. The mean delivery time B. The standard deviation of the delivery time C. the number of deliveries that took less than 6 hours D. the proportion of deliveries that took less than 6 hours

A. The mean delivery time

The national average for an 8th grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school districts claim, how does one define the population parameter of interest? A. The mean score on the eight-grade reading comprehension test. B. The number of eight graders who took the reading comprehension test C. The standard deviation of the score on the eight-grade reading comprehension test D. The proportion of eight graders who scored above 73 on the reading comprehension test

A. The mean score on the eight-grade reading comprehension test.

Which of the following is considered an estimator? A. X bar B. u C. o sigma a (squared)

A. X bar

Consider the following hypothesis that relate to the medical field. Ho A person is free of disease HA A person has disease In this instance, a type 1 error is often referred to as A. a false positive B. A false negative C. a negative result D. the power of the test

A. a false positive

Hypotheses can be right tailed, left tailed or two tailed A. true B. false

A. true

Hypotheses test population parameters such as the mean or proportion A. true B. false

A. true

Which of the following meets the requirements of a simple random sample? A. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample B. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. C. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age. D. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.

B. A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age.

For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when o is known? A. If the sample standard deviation is smaller, the interval is wider B. If the population, standard deviation is greater, the interval is wider C. If the population standard deviation is smaller, the interval is wider D. If the population standard deviation is greater, the interval is narrower.

B. If the population, standard deviation is greater, the interval is wider

What is the most typical form of a calculated confidence interval? A. Point estimate = standard error B. Point estimate = Margin of error C. Population parameter = Standard error D. Population parameter = Margin of error

B. Point estimate = Margin of error

The alternative hypothesis typically A. Corresponds to the presumed default state of nature B. contests the status quo, for which a corrective action may be required C. States the probability of rejecting the null hypothesis when it is false D. States the probability of rejecting the null hypothesis when it is true

B. contests the status quo, for which a corrective action may be required

Selection bias occurs when A. the population has been divided into strata B. portions of the population are excluded from the consideration for the sample C. cluster sampling is used instead of stratified random sampling D. those responding to a survey or poll differ systematically from the nonrespondents

B. portions of the population are excluded from the consideration for the sample

The t(df) distribution is similar to the z distribution because? A. as the degrees of freedom go to infinity, the t distribution converges to the z distribution, but both do not have asymptomatic tails. B. both have asymptotic tails that is, their tails become closer and closer to the horizontal axis and eventually cross the axis C. as the degrees of freedom go to infinity, the t distribution converges to the z distribution and both have asymptotic tails, that is their tails become closer and closer to the horizontal axis but never touch it. D. Neither as the degrees of freedom go to infinity, the t distribution converges to the z distribution nor both have asymptotic tails that is, their tails become closer and closer to the horizontal axis but never touch it.

C. as the degrees of freedom go to infinity, the t distribution converges to the z distribution and both have asymptotic tails, that is their tails become closer and closer to the horizontal axis but never touch it.

Statistics are used to estimate population parameters particularly when it is impossible or too expensive to poll an entire population. A particular value of a statistic is referred to as a(n) A. Mean B. Stratum C. estimate D. finite correction factor

C. estimate

Which of the following meets the requirements of a stratified random sample? A) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people who volunteer for the sample. B) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six people chosen at random, without regard to age. C) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include six males chosen at random, without regard to age. D) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.

D) A population contains 10 members under the age of 25 and 20 members over the age of 25. The sample will include two people chosen at random under the age of 25 and four people chosen at random over 25.

A tutor promises to improve GMAT scores of students by more than 50 points after three lessons. To see if this is true, the tutor takes a sample of 49 students' test scores after and before they received tutoring. Which of the following hypotheses will determine if the students improved their test scores by more than 50 points after being tutored? A) H0: µD ≥ 50, HA: µD < 50 B) H0: µD ≥ 0, HA: µD < 0 C) H0: µD ≤ 0, HA: µD > 0 D) H0: µD ≤ 50, HA: µD > 50

D) H0: µD ≤ 50, HA: µD > 50

Which of the following is true about statistics such as the sample mean or sample proportion? A. A statistic is a constant B. A statistic is always known C. A statistic is a parameter D. A statistic is a random variable

D. A statistic is a random variable

When comparing two population means, their hypothesized difference _____ A. Must be negative B. Must be positive C. Must be zero D. May assume any value

D. May assume any value

In general, the null and alternative hypotheses are A. Additive B. Correlated C. Multiplicative D. Mutually exclusive

D. Mutually exclusive

Which of the following types of tests may be performed? A. Right-tailed and two tailed tests B. Left tailed and two-tailed tests C. Right-tailed and left tailed tests D. Right-tailed, left tailed, and two-tailed tests

D. Right-tailed, left tailed, and two-tailed tests

A sample of a given size is used to construct a 95% confidence interval for the population mean with a known population standard deviation. If a bigger sample had been used instead, then the 95% confidence interval would have been __________ and the probability of making an error would have been _________ A. Wider, smaller B. narrower, smaller C. Wider, unchanged D. narrower, unchanged

D. narrower, unchanged

Two or more random samples are considered independent if _____ A. The process that generates one sample is the same as the process that generates the other sample B. the process that generates one sample is related to the process that generates the other sample C. the process that generates one sample is influenced by the process that generates the other sample D. the process that generates one sample is completely separate from the process that generates the other sample

D. the process that generates one sample is completely separate from the process that generates the other sample

Bias can occur in sampling. Bias refers to _______. A. the division of the population into overlapping groups B. the creation of strata, which are proportional to the stratum's size C. the use of cluster sampling instead of stratified random sampling D. the tendency of a sample statistic to systematically over- or underestimate a population parameter

D. the tendency of a sample statistic to systematically over- or underestimate a population parameter

Nonresponse bias occurs when A. the population has been divided into strata B. portions of the population are excluded from the sample C. cluster sampling is used instead of stratified random sampling D. those responding to a survey or poll differ systematically from the nonrespondents

D. those responding to a survey or poll differ systematically from the nonrespondents

A bank is trying to determine which model of safe to install. The bank manager believes that each model is equally resistant to safe crackers, but sets up a test to be sure. He hires nine safe experts to break into each of the models, timing each endeavor. The results (in seconds) are given next, paired by expert. Let D be the difference: Time to break Safe 1 minus Time to break Safe 2.

Ho uD = 0 HA uD = 0

Stratified sampling vs cluster sampling

Stratified sampling - sample consist of elements from each group preferred when the objective is to increase precision Cluster sampling - sample consist of elements from the selected groups, sample every observation in the randomly selected clusters

Population

consists of all items of interest in a statistical problem

Simple random sample

every member of the population has a known and equal chance of selection. Simple random sample is a sample of observations which has the same probability of being selected from the population as any other sample of observations

Bias

the tendency of a sample statistic to systematically over or underestimate a population parameter