STATS UNIT 3 EXAM
Over the entire six years that students attend an Ohio elementary school, they are absent, on average, 28 days due to influenza. Assume that the standard deviation over this time period is σ = 9 days. Upon graduation from elementary school, a random sample of 36 students is taken and asked how many days of school they missed due to influenza. What is the expected value for the sampling distribution of the average number of school days missed due to influenza? a) 28 b) 6 c) 9 d) 168
a) 28
The daily revenue from the sale of fried dough at a local street vendor in Boston is known to be normally distributed with a known standard deviation of $120. The revenue on each of the last 25 days is noted, and the average is computed as $550. Construct a 95% confidence interval for the population mean of the sale of fried dough by this vendor. a) 550 ± 1.96(120/5) b) 550 ± 1.645(120/5) c) 120 ± 1.96(550/5) d) 120 ± 1.645(550/5)
a) 550 ± 1.96(120/5)
A hypothesis test regarding the population mean is based on __________. a) the sampling distribution of the sample mean b) the sampling distribution of the sample proportion c) the sampling distribution of the sample standard deviation d) the sampling distribution of the sample variance
a) the sampling distribution of the sample mean
Which of the following is considered an estimate? a) x̄ = 20 b) σ = 3.2 c) σ^2 =10 d) μ= 12
a) x̄ = 20
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 chosen at random, without regard to age. 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 who volunteer for the sample. c) 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 six males chosen at random, without regard to age.
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 chosen at random, without regard to age.
What type of test for population means should be performed when employees are first tested, trained, and then retested? a) A t test under dependent sampling. b) A z test under independent sampling with known population variances. c) A t test under independent sampling with unknown but equal population variances. d) A t test under independent sampling with unknown and unequal population variances.
a) A t test under dependent sampling.
What type of data is required to compare prices of the same textbooks sold by two different vendors? a) Dependent random samples with numerical data. b) Independent random samples with numerical data. c) Independent random samples with categorical data. d) Dependent random samples with categorical data.
a) Dependent random samples with numerical data.
A 99% confidence interval for the population mean yields the following results: [−3.79, 5.86]. At the 1% significance level, what decision should be made regarding the following hypothesis test with H0:μ = 0,HA:μ ≠ 0? a) Do not reject H0; we cannot conclude that the mean differs from zero. b) Do not reject H0; we can conclude that the mean differs from zero. c) Reject H0; we cannot conclude that the mean differs from zero. d) Reject H0; we can conclude that the mean differs from zero.
a) Do not reject H0; we cannot conclude that the mean differs from zero.
For a given confidence level and sample size, which of the following is true in the interval estimation of the population mean when σ is known? a) If the population standard deviation is greater, the interval is wider. b) If the sample standard deviation is smaller, 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.
a) If the population standard deviation is greater, the interval is wider.
How do the tdf and z distributions differ? a) The tdf distribution has broader tails (it is flatter around zero). b) There is no difference between the tdf and z distributions; they both do not have asymptomatic tails. c) The z distribution has asymptotic tails, while the tdf distribution does not. d) The z distribution has broader tails (it is flatter around zero).
a) The tdf distribution has broader tails (it is flatter around zero).
Which of the following statements regarding the sampling distribution of the sample mean is TRUE? a) The variance of the sample mean is smaller than the variance of all individual observations in the population. b) The variance of the sample mean is equal to the variance of all individual observations in the population. c) The expected value of the sample mean from a large sample is smaller than that from a small sample. d) The expected value of the sample mean from a large sample is greater than that from a small sample.
a) The variance of the sample mean is smaller than the variance of all individual observations in the population.
Which of the following is considered an estimator? a) X̄ b) σ^2 c) σ d) µ
a) X̄
Statisticians like precision in their interval estimates. A low margin of error is needed to achieve this. Which of the following supports this when selecting sample sizes? a) a larger sample size reduces the margin of error b) a smaller sample size reduces the margin of error c) a sample size has no impact on the margin of error d) a larger sample size increases the margin of error
a) a larger sample size reduces the margin of error
When we reject the null hypothesis when it is actually false, we have committed __________. a) no error b) a Type I error c) a Type II error d) a Type I error and a Type II error
a) no error
If the p-value for a hypothesis test is 0.07 and the chosen level of significance is α = 0.05, then the correct conclusion is to __________. a) not reject the null hypothesis b) reject the null hypothesis c) not reject the null hypothesis if σ = 10 d) reject the null hypothesis if σ = 10
a) not reject the null hypothesis
A Type I error occurs when we __________. a) reject the null hypothesis when it is actually true b) reject the null hypothesis when it is actually false c) do not reject the null hypothesis when it is actually true d) do not reject the null hypothesis when it is actually false
a) reject the null hypothesis when it is actually true
When testing the difference between two population means under independent sampling, we use the z distribution if _________ . a) the population variances are know b) the population variances are unknown, but assumed to be equal c) the population variances are unknown and cannot be assumed equal d) Both the population variances are known and the population variances are unknown, but assumed to be equal
a) the population variances are know
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. If a 99% confidence interval is constructed instead of a 95% confidence interval for the population mean, then __________. a) the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease b) the resulting margin of error will decrease and the risk of reporting an incorrect interval will decrease c) the resulting margin of error will increase and the risk of reporting an incorrect interval will increase d) the resulting margin of error will decrease and the risk of reporting an incorrect interval will increase
a) the resulting margin of error will increase and the risk of reporting an incorrect interval will decrease
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 two people chosen at random from each city block. b) A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks. c) 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. d) 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.
b) A population can be divided into 50 city blocks. The sample will include residents from two randomly chosen city blocks.
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 chosen at random, without regard to age. b) 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. 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 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 two people chosen at random under the age of 25 and four people chosen at random over 25.
For a given confidence level and population standard deviation, which of the following is true in the interval estimation of the population mean? a) If the population size is bigger, the interval is narrower. b) If the sample size is bigger, the interval is narrower. c) If the population size is smaller, the interval is narrower. d) If the sample size is smaller, the interval is narrower.
b) If the sample size is bigger, the interval is narrower.
Which of the following is not a form of bias? a) Those responding to a survey or poll differ systematically from the nonrespondents. b) Information from the sample is typical of information in the population. c) Information from the sample overemphasizes a particular stratum of the population. d) Portions of the population are excluded from the sample.
b) Information from the sample is typical of information in the population.
Which of the following is not a restriction for comparing two population means? a) A normally distributed sampling distribution of X̄1−X̄2 b) Matched-pairs sampling c) Independent random samples d) Equal or unequal variances
b) Matched-pairs sampling
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 ± Margin of error d) Population parameter ± Standard error
b) Point estimate ± Margin of error
When conducting a hypothesis test, which of the following decisions represents an error? a) Not rejecting the null hypothesis when it is true. b) Rejecting the null hypothesis when it is true. c) Rejecting the null hypothesis when it is false and not rejecting the null hypothesis when it is true. d) Rejecting the null hypothesis when it is false.
b) Rejecting the null hypothesis when it is true.
What conditions are required by the central limit theorem before a confidence interval of the population mean may be created? a) The underlying population must be normally distributed. b) The underlying population need not be normally distributed if the sample size is 30 or more. c) The underlying population need not be normally distributed if the population standard deviation is known. d) The underlying population must be normally distributed if the sample size is 30 or more.
b) The underlying population need not be normally distributed if the sample size is 30 or more.
What is the purpose of calculating a confidence interval? a) To provide a range of values that, with a certain measure of confidence, contains the sample statistic of interest. b) To provide a range of values that, with a certain measure of confidence, contains the population parameter of interest. c) To provide a range of values that has a certain large probability of containing the population parameter of interest. d) 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 population parameter of interest.
When calculating the standard error of X̄1−X̄2 , under what assumption do you pool the sample variances s2/2and s2/2? a) Known population variances. b) Unknown population variances that are assumed equal. c) Unknown population variances that are assumed unequal. d) The two sample means are derived from two dependent populations.
b) Unknown population variances that are assumed equal.
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 true d) states the probability of rejecting the null hypothesis when it is false
b) contests the status quo, for which a corrective action may be required
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) stratum b) estimate c) mean d) finite correction factor
b) estimate
In general, the null and alternative hypotheses are __________. a) correlated b) mutually exclusive c) multiplicative d) additive
b) mutually exclusive
If the underlying populations cannot be assumed to be normal, then by the central limit theorem, the sampling distribution of X̄1 - X̄2 is approximately normal only if both sample sizes are sufficiently large—that is, when _________ . a) n1 + n2 = 30 b) n1 ≥ 30 and n2 ≥ 30 c) n1 = 30 and n2 = 30 d) n1 + n2 ≥ 30
b) n1 ≥ 30 and n2 ≥ 30
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) do not reject the null hypothesis and conclude that the mean IQ is not greater than 100 b) reject the null hypothesis and conclude that the mean IQ is greater than 100 c) do not reject the null hypothesis and conclude that the mean IQ is greater than 100 d) reject the null hypothesis and conclude that the mean IQ is not greater than 100
b) reject the null hypothesis and conclude that the mean IQ is greater than 100
A local courier service advertises that its average delivery time is less than 6 hours for local deliveries. When testing the two hypotheses, H0: μ ≥ 6 and HA: μ < 6, μ stand for __________. a) the number of deliveries that took less than 6 hours b) the mean delivery time c) the standard deviation of the delivery time d) the proportion of deliveries that took less than 6 hours
b) the mean delivery time
Two or more random samples are considered independent if _________ . a) the process that generates one sample is influenced by the process that generates the other sample b) the process that generates one sample is completely separate from the process that generates the other sample c) the process that generates one sample is the same as the process that generates the other sample d) the process that generates one sample is related to the process that generates the other sample
b) the process that generates one sample is completely separate from the process that generates the other sample
According to the central limit theorem, the distribution of the sample means is normal if ________. a) the standard deviation of the population is known b) the sample size n ≥ 30 c) both the underlying population is normal and the sample size n ≥ 30 are correct d) the underlying population is normal
b) the sample size n ≥ 30
If the chosen significance level is α = 0.05, then __________. a) there is a 5% probability of rejecting a false null hypothesis b) there is a 5% probability of rejecting a true null hypothesis c) there is a 5% probability of accepting a false null hypothesis d) there is a 5% probability of accepting a true null hypothesis
b) there is a 5% probability of rejecting a true null hypothesis
What is zα / 2 for a 95% confidence interval of the population mean? a) 0.49 b) 1.645 c) 1.96 c) 0.48
c) 1.96
The ages of MBA students at a university are normally distributed with a known population variance of 10.24. Suppose you are asked to construct a 95% confidence interval for the population mean age if the mean of a sample of 36 students is 26.5 years. What is the margin of error for a 95% confidence interval for the population mean? a) 1.96(10.24/6) b) 1.645(3.20/6) c) 1.96(3.20/6) d) 1.645(10.24/6)
c) 1.96(3.20/6)
A particular personal trainer works primarily with track and field athletes. She believes that her clients run faster after going through her program for six weeks. How might she test that claim? a) A hypothesis test for p1 −p2 . b) A hypothesis test for μ1−μ2· c) A matched-pairs hypothesis test for μD. d) We are unable to conduct a hypothesis test because the samples would not be independent.
c) A matched-pairs hypothesis test for μD.
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 random variable. d) A statistic is a parameter.
c) A statistic is a random variable.
If a population is known to be normally distributed, what can be said of the sampling distribution of the sample mean drawn from this population? a) For a sample size n < 30, the sampling distribution of the sample mean is normally distributed. b) For a sample size n > 30, the sampling distribution of the sample mean is normally distributed. c) For any sample size n, the sampling distribution of the sample mean is normally distributed. d) For a sample size n < 50, the sampling distribution of the sample mean is normally distributed.
c) For any sample size n, the sampling distribution of the sample mean is normally distributed.
A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides his six lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results. Which of the following are the appropriate competing hypotheses? a) H0: µD ≠ 0, HA: µD = 0 b) H0: µD ≤ 0, HA: µD > 0 c) H0: µD = 0, HA: µD ≠ 0 d) H0: µD ≥ 0, HA: µD < 0
c) H0: µD = 0, HA: µD ≠ 0
For a given sample size and population standard deviation, which of the following is true in the interval estimation of the population mean? a) If the confidence level is smaller, the interval is wider. b) If the confidence level is smaller, the interval is less precise. c) If the confidence level is greater, the interval is wider. d) If the confidence level is greater, the interval is more precise.
c) If the confidence level is greater, the interval is wider.
Suppose you want to perform a test to compare the mean GPA of all freshmen with the mean GPA of all sophomores in a college? What type of sampling is required for this test? a) Matched-pairs sampling with numerical data b) Matched-pairs sampling with categorical data c) Independent sampling with numerical data d) Independent sampling with categorical data
c) Independent sampling with numerical data
How does the variance of the sample mean compare to the variance of the population? a) It is larger and therefore suggests that averages have more variation than individual observations. b) It is larger and therefore suggests that averages have less variation than individual observations. c) It is smaller and therefore suggests that averages have less variation than individual observations. d) It is smaller and therefore suggests that averages have more variation than individual observations.
c) It is smaller and therefore suggests that averages have less variation than individual observations.
John would like to conduct a survey in his neighborhood to get homeowners' opinion on the Delmarva proposal to switch to natural gas. Which of the following is an example of a stratified sample? a) John selects the first 25 homes that he passes as he walks into the entrance of the development. b) John randomly chooses three streets and selects every third house on those streets. c) John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group. d) John selects every third house on each street.
c) John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group.
Peggy would like to conduct a survey in her neighborhood to get homeowners' opinions on the Delmarva proposal to switch to natural gas. Which of the following is an example of a convenience sample? a) John divides the population into two-story, split-level, and ranch houses. Then, he selects a proportional number of houses from each group. b) John selects every third house on each street. c) John selects the first 25 homes that he passes as he walks into the entrance of the development. d) John randomly chooses three streets and selects every third house on those streets.
c) John selects the first 25 homes that he passes as he walks into the entrance of the development.
What is the decision rule when using the p-value approach to hypothesis testing? a) Do not reject H0 if the p-value > 1 − α. b) Reject H0 if the p-value > α. c) Reject H0 if the p-value < α. d) Do not reject H0 if the p-value < 1 − α.
c) Reject H0 if the p-value < α.
When the required sample size calculated by using a formula is not a whole number, what is the best choice for the required sample size? a) Round the result of the calculation up to the nearest whole number plus one. b) Round the result of the calculation down to the nearest whole number. c) Round the result of the calculation up to the nearest whole number. d) Round the result of the calculation down to the nearest whole number minus one.
c) Round the result of the calculation up to the nearest whole number.
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy in a sample of 36 cereal boxes: the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pounds. Which of the following conclusions is correct with a 95% confidence level? a) There is not enough information to make a conclusion. b) The machine is operating improperly because the target is above the upper limit. c) The machine is operating properly because the interval contains the target. d) The machine is operating improperly because the target is below the lower limit.
c) The machine is operating properly because the interval contains the target.
A survey is designed to collect data on students' evaluations of their instructor's teaching performance. Which of the following situations most likely results in social-desirability biases? a) The survey takes over thirty minutes to complete. b) The survey is conducted during the first week of class. c) The survey is administered in class with the instructor in the room the entire time. d) The survey is mailed to students' home address during exam week.
c) The survey is administered in class with the instructor in the room the entire time.
The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean ______. a) becomes smaller b) is closer to the standard deviation c) is closer to a normal distribution d) becomes larger
c) is closer to a normal distribution
Which of the following is the necessary condition for creating confidence intervals for the population mean? a) known population parameter b) known standard deviation of the estimator c) normality of the estimator d) normality of the population
c) normality of the estimator
When conducting a hypothesis test for a given sample size, if the probability of a Type I error decreases, then the __________. a) probability of Type II error decreases b) probability of incorrectly rejecting the null hypothesis increases c) probability of incorrectly not rejecting the null hypothesis increases d) probability of incorrectly not rejecting the null hypothesis decreases
c) probability of incorrectly not rejecting the null hypothesis increases
If the p-value for a hypothesis test is 0.027 and the chosen level of significance is α = 0.05, then the correct conclusion is to __________. a) not reject the null hypothesis if σ = 10 b) reject the null hypothesis if σ = 10 c) reject the null hypothesis d) not reject the null hypothesis
c) reject the null hypothesis
The owner of a large car dealership believes that the financial crisis decreased the number of customers visiting her dealership. The dealership has historically had 800 customers per day. The owner takes a sample of 100 days and finds the average number of customers visiting the dealership per day was 750. Assume that the population standard deviation is 350. The population parameter to be tested is __________. a) the average number of 750 customers per day b) the proportion of customers visiting the dealership per day c) the mean number of customers visiting the dealership per day d) the standard deviation of the number of customers visiting the dealership per day
c) the mean number of customers visiting the dealership per day
Nonresponse bias occurs when ______. a) portions of the population are excluded from the sample b) the population has been divided into strata c) those responding to a survey or poll differ systematically from the nonrespondents d) cluster sampling is used instead of stratified random sampling
c) those responding to a survey or poll differ systematically from the nonrespondents
What is zα/2 for a 90% confidence interval of the population mean? a) 0.48 b) 1.96 c) 0.49 d) 1.645
d) 1.645
Which of the following is an example about analyzing the difference between two population means? a) Compare the average checkout time at ABC Supermarket against what is being advertised. b) Compare the proportion of defects found in a sample of 10 chips versus a sample of 100 chips. c) Compare the average number of defects against the control limits of the control chart. d) Compare the average six-year graduation rate between private and public colleges.
d) Compare the average six-year graduation rate between private and public colleges.
Which of the following is NOT an example of analyzing the mean difference of two populations based on matched-pairs sampling? a) Compare the mean wait time of customers being served at a bank in a branch that is fully automated versus one that is 10% automated. b) Compare the mean wait time of customers being served at a bank before and after the use of chatbots. c) Compare the mean wait time of customers being served at a bank before and after the remodeling. d) Compare the mean wait time of customers being served at a bank before and after the weekend.
d) Compare the mean wait time of customers being served at a bank before and after the weekend.
An analyst takes a random sample of 25 firms in the telecommunications industry and constructs a confidence interval for the mean return for the prior year. Holding all else constant, if he increased the sample size to 30 firms, how are the standard error of the mean and the width of the confidence interval affected? a) C b) B c) A d) D
d) D
A 7,000-seat theater is interested in determining whether there is a difference in attendance between shows on Tuesday evening and those on Wednesday evening. A random sample of 25 weeks is collected for Tuesday; a different sample of 25 weeks is collected for Wednesday. The mean attendance on Tuesday evening is calculated as 5,500, while the mean attendance on Wednesday evening is calculated as 5,850. The known population standard deviation for attendance on Tuesday evening is 550 and the known population standard deviation for attendance on Wednesday evening is 445. Let μ1 be the population mean of Tuesday, μ2 be the population mean of Wednesday, and μD be the mean difference for a matched-pairs sampling. What are the appropriate hypotheses to determine whether there is a difference, on average, in attendance between shows on Tuesday evening and Wednesday evening? a) H0: µD = 0, HA: µD ≠ 0 b) H0: µD ≥ 0, HA: µD < 0 c) H0: µ1 − µ2 ≥ 0, HA: µ1 − µ2 < 0 d) H0: µ1 − µ2 = 0, HA: µ1 − µ2 ≠ 0
d) H0: µ1 − µ2 = 0, HA: µ1 − µ2 ≠ 0
A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let µ1 and µ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Specify the competing hypotheses to determine if fertilizer A contains more nitrogen per batch than fertilizer B. a) H0: µ1 − µ2 = 0, HA: µ1 − µ2 ≠ 0 b) H0: p1 − p2 ≤ 0, HA: p1 − p2 > 0 c) H0: µ1 − µ2 ≥ 0, HA: µ1 − µ2 < 0 d) H0: µ1 − µ2 ≤ 0, HA: µ1 − µ2 > 0
d) H0: µ1 − µ2 ≤ 0, HA: µ1 − µ2 > 0
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. Which of the following hypotheses will determine if the two safes take, on average, the same amount of time to crack? a) H0: µD ≥ 0, HA: µD < 0 b) H0: µD ≤ 0, HA: µD > 0 c) H0: µD ≠ 0, HA: µD = 0 d) H0: µD = 0, HA: µD ≠ 0
d) H0: µD = 0, HA: µD ≠ 0
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
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. The mean difference was 53 points better after tutoring, with a standard deviation of the difference equal to 12 points. Let µD denote the mean of the difference: score after tutoring minus score before 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 ≤ 0, HA: µD > 0 b) H0: µD ≥ 50, HA: µD < 50 c) H0: µD ≥ 0, HA: µD < 0 d) H0: µD ≤ 50, HA: µD > 50
d) H0: µD ≤ 50, HA: µD > 50
A new sales training program has been instituted at a rent-to-own company. Prior to the training, 10 employees were tested on their knowledge of products offered by the company. Once the training was completed, the employees were tested again in an effort to determine whether the training program was effective. Scores are known to be normally distributed. The sample scores on the tests are listed next. Use pretest score as µ1 for population 1 and posttest score as µ2 for population 2, or µD as the mean of the difference calculated as pretest score minus posttest score. Which of the following are the appropriate hypotheses to determine if the training increases scores? a) H0: µ1 − µ2 ≤ 0, HA: µ1 − µ2 > 0 b) H0: µD ≤ 0, HA: µD > 0 c) H0: µ1 − µ2 ≥ 0, HA: µ1 − µ2 < 0 d) H0: µD ≥ 0, HA: µD < 0
d) H0: µD ≥ 0, HA: µD < 0
Which of the following set of hypotheses is used to test if the mean of the first population is smaller than the mean of the second population, using matched-paired sampling? a) H0: µD ≤ 0, HA: µD > 0 b) H0: µ1 − µ2 ≥ 0, HA: µ1 − µ2 < 0 c) H0: µ1 − µ2 ≤ 0, HA: µ1 − µ2 > 0 d) H0: µD ≥ 0,HA: µD < 0
d) H0: µD ≥ 0,HA: µD < 0
The national average for an eighth-grade reading comprehension test is 73. A school district claims that its eighth-graders outperform the national average. In testing the school district's claim, how does one define the population parameter of interest? a) The standard deviation of the score on the eighth-grade reading comprehension test b) The number of eighth graders who took the reading comprehension test c) The proportion of eighth graders who scored above 73 on the reading comprehension test d) The mean score on the eighth-grade reading comprehension test
d) The mean score on the eighth-grade reading comprehension test
Confidence intervals of the population mean may be created for the cases when the population standard deviation is known or unknown. How are these two cases treated differently? a) Use the z table when σ is unknown; use the t table when σ is known. b) Use the z table when s is known; use the t table when s is unknown. c) Use the z table when s is unknown; use the t table when s is known. d) Use the z table when σ is known; use the t table when σ is unknown.
d) Use the z table when σ is known; use the t table when σ is unknown.
Consider the following hypotheses that relate to the medical field: H0: A person is free of disease. HA: A person has disease. In this instance, a Type I error is often referred to as __________. a) a false negative b) a negative result c) the power of the test d) a false positive
d) a false positive
The tdf distribution is similar to the z distribution because __________. a) both have asymptotic tails—that is, their tails become closer and closer to the horizontal axis and eventually cross the axis b) as the degrees of freedom go to infinity, the t distribution converges to the z distribution, but both do not have asymptomatic tails c) 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 d) 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) 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
For a given sample size n, __________. a) decreasing the probability of a Type I error α will decrease the probability of a Type II error β b) increasing the probability of a Type I error α will increase the probability of a Type II error β as long as σ is known c) changing the probability of a Type I error α will have no impact on the probability of a Type II error β d) decreasing the probability of a Type I error α will increase the probability of a Type II error β
d) decreasing the probability of a Type I error α will increase the probability of a Type II error β
A Type II error occurs when we __________. a) do not reject the null hypothesis when it is actually true b) reject the null hypothesis when it is actually false c) reject the null hypothesis when it is actually true d) do not reject the null hypothesis when it is actually false
d) do not reject the null hypothesis when it is actually false
When comparing two population means, their hypothesized difference _________ . a) must be positive b) must be zero c) must be negative d) may assume any value
d) may assume any value
Selection bias occurs when ______. a) cluster sampling is used instead of stratified random sampling b) the population has been divided into strata c) those responding to a survey or poll differ systematically from the nonrespondents d) portions of the population are excluded from the consideration for the sample
d) portions of the population are excluded from the consideration for the sample
If the null hypothesis is rejected at a 1% significance level, then __________. a) the alternative hypothesis will be rejected at a 5% significance level b) the alternative hypothesis will not be rejected at a 5% significance level c) the null hypothesis will not be rejected at a 5% significance level d) the null hypothesis will be rejected at a 5% significance level
d) the null hypothesis will be rejected at a 5% significance level
The choice of an appropriate test for comparing two population means depends on whether we deal with the following except: a) categorical or numerical data b) independent or matched-pairs sampling c) the equality or lack of equality of population variances d) the sum or product of a single parameter
d) the sum or product of a single parameter
A 90% confidence interval is constructed for the population mean. If a 95% confidence interval had been constructed instead (everything else remaining the same), the width of the interval would have been ________ and the probability of making an error would have been _________. a) narrower; bigger b) wider; bigger c) narrower; smaller d) wider; smaller
d) wider; smaller
