ISDS 2000 Exam 2
A random sample of size 36 is taken from a population with mean µ = 17 and standard deviation σ = 6. What are the expected value and the standard deviation for the sampling distribution of the sample mean? A) 0.425 and 1.00 B) 0.425 and 2.83 C) 17 and 1.00 D) 17 and 2.83
C) 17 and 1.00
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
Suppose that, on average, electricians earn approximately µ = $54,000 per year in the United States. Assume that the distribution for electricians' yearly earnings is normally distributed and that the standard deviation is σ = $12,000. What is the probability that the average salary of four randomly selected electricians exceeds $60,000? A) 0.1587 B) 0.3085 C) 0.6915 D) 0.8413
A) 0.1587
The labor force participation rate is the number of people in the labor force divided by the number of people in the country who are of working age and not institutionalized. The BLS reported in February 2012 that the labor force participation rate in the United States was 63.7% (Calculatedrisk.com). A marketing company asks 120 working-age people if they either have a job or are looking for a job, or, in other words, whether they are in the labor force. What is the probability that fewer than 60% of those surveyed are members of the labor force? A) 0.1996 B) 0.7995 C) 0.8400 D) 0.9706
A) 0.1996
A nursery sells trees of different types and heights. These trees average 60 inches in height with a standard deviation of 16 inches. Suppose that 75 pine trees are sold for planting at City Hall. What is the standard deviation for the sample mean? A) 1.85 B) 3.41 C) 4 D) 16
A) 1.85
A university is interested in promoting graduates of its honors program by establishing that the mean GPA of these graduates exceeds 3.50. A sample of 36 honors students is taken and is found to have a mean GPA equal to 3.60. The population standard deviation is assumed to equal 0.40. To establish whether the mean GPA exceeds 3.50, the appropriate hypotheses are ______________. A) Ho:μ≤3.50,HA:μ>3.50 B) Ho:X−≤3.50,HA:X−>3.50 C) Ho:μ≥3.50,HA:μ<3.50 D) Ho:X−≥3.50,HA:X−<3.50
A) Ho:μ≤3.50,HA:μ>3.50
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 mean score on the eighth-grade reading comprehension test B) The number of eighth graders who took the reading comprehension test C) The standard deviation of the score on the eighth-grade reading comprehension test D) The proportion of eighth graders who scored above 73 on the reading comprehension test
A) The mean score on the eighth-grade reading comprehension test
A professional sports organization is going to implement a test for steroids. The test gives a positive reaction in 94% of the people who have taken the steroid. However, it erroneously gives a positive reaction in 4% of the people who have not taken the steroid. What is the probability of Type I and Type II errors giving the null hypothesis "the individual has not taken steroids." A) Type I: 4%, Type II: 6% B) Type I: 6%, Type II: 4% C) Type I: 94%, Type II: 4% D) Type I: 4%, Type II: 94%
A) Type I: 4%, Type II: 6%
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) reject the null hypothesis B) not reject the null hypothesis C) reject the null hypothesis if σ = 10 D) not reject the null hypothesis if σ = 10
A) reject the null hypothesis (The decision rule is to reject the null hypothesis if the p-value <α and not reject the null hypothesis if the p-value ≥ α.)
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
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
It is generally believed that no more than 0.50 of all babies in a town in Texas are born out of wedlock. A politician claims that the proportion of babies born out of wedlock is increasing. When testing the two hypotheses, H0>: p ≤ 0.50 and HA: p > 0.50, p stands for _____________. A) the current proportion of babies born out of wedlock B) the mean number of babies born out of wedlock C) the number of babies born out of wedlock D) the general belief that the proportion of babies born out of wedlock is no more than 0.50
A) the current proportion of babies born out of wedlock
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 value of the test statistic is ____________. A) z = -1.429 B) t99 = -1.429 C) z = 1.429 D) t99 = 1.429
A) z= -1.429
A university administrator expects that 25% of students in a core course will receive an A. He looks at the grades assigned to 60 students. The probability that the proportion of students who receive an A is not between 0.20 and 0.30 is ______. A) 0.1867 B) 0.3711 C) 0.6266 D) 0.8133
B) 0.3711
Suppose the average math SAT score for students enrolled at local community college is 490.4 with a standard deviation of 63.7. A random sample of 49 students has been selected. The standard error of the mean for this sample is ______. A) 10.6 B) 9.1 C) 63.7 D) 28.4
B) 9.1
Which of the following are two-tailed tests? A) Ho:μ ≤ 10, HA:μ > 10 B) Ho:μ = 10, HA:μ ≠ 10 C) Ho:μ ≥ 400, HA:μ < 400 D) Both Ho:μ ≤ 10, HA:μ > 10 and Ho:μ ≥ 400, HA:μ < 400
B) Ho:μ = 10, HA:μ ≠ 10
What is the decision rule when using the p-value approach to hypothesis testing? A) Reject Ho if the p-value > α. B) Reject Ho if the p-value < α. C) Do not reject Ho if the p-value < 1 - α. D) Do not reject Ho if the p-value > 1 - α.
B) Reject Ho if the p-value < α.
A fast-food franchise is considering building a restaurant at a busy intersection. A financial advisor determines that the site is acceptable only if, on average, more than 300 automobiles pass the location per hour. The advisor tests the following hypotheses: Ho: μ ≤ 300. HA: μ > 300. The consequences of committing a Type I error would be that____________________________. A) the franchiser builds on an acceptable site B) the franchiser builds on an unacceptable site C) the franchiser does not build on an acceptable site D) the franchiser does not build on an unacceptable site
B) the franchiser builds on an unacceptable site
According to the 2011 Gallup daily tracking polls (www.gallup.com, February 3, 2012), Mississippi is the most conservative U.S. state, with 53.4 percent of its residents identifying themselves as conservative. What is the probability that at least 100 but fewer than 115 respondents of a random sample of 200 Mississippi residents identify as conservative? A) 0.1685 B) 0.3370 C) 0.7099 D) 0.8770
C) 0.7099
Expedia would like to test if the average round-trip airfare between Philadelphia and Dublin is less than $1,200. The correct hypothesis statement would be __________________________. A) Ho:μ≠$1,200,HA:μ=$1,200 B) Ho:μ<$1,200,HA:μ≥$1,200 C) Ho:μ≥$1,200,HA:μ<$1,200 D) Ho:μ=$1,200,HA:μ≠$1,200
C) Ho:μ≥$1,200,HA:μ<$1,200
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
The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution of the sample mean ______. A) becomes larger B) becomes smaller C) is closer to a normal distribution D) is closer to the standard deviation
C) is closer to a normal distribution
A newly hired basketball coach promised a high-paced attack that will put more points on the board than the team's previously tepid offense historically managed. After a few months, the team owner looks at the data to test the coach's claim. He takes a sample of 36 of the team's games under the new coach and finds that they scored an average of 101 points with a standard deviation of 6 points. Over the past 10 years, the team had averaged 99 points. What is the value of the appropriate test statistic to test the new coach's claim at the 1% significance level? A) t35 = 0.33 B) z = 0.33 C) t35 = 2.00 D) z = 2.00
C) t35 = 2.00
A random sample of size 100 is taken from a population described by the proportion p = 0.60. What are the expected value and the standard error for the sampling distribution of the sample proportion? A) 0.006 and 0.0024 B) 0.060 and 0.049 C) 0.600 and 0.0024 D) 0.600 and 0.049
D) 0.600 and 0.049
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. The probability that the sample mean is less than 30 school days is ______. A) 0.0918 B) 0.4129 C) 0.5871 D) 0.9088
D) 0.9088
Professor Elderman has given the same multiple-choice final exam in his Principles of Microeconomics class for many years. After examining his records from the past 10 years, he finds that the scores have a mean of 76 and a standard deviation of 12. What is the probability that a class of 36 students will have an average greater than 70 on Professor Elderman's final exam? A) 0.0014 B) 0.3085 C) 0.6915 D) 0.9986
D) 0.9986
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.
In general, the null and alternative hypotheses are __________. A) additive B) correlated C) multiplicative D) mutually exclusive
D) mutually exclusive
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
When conducting a hypothesis test concerning the population mean, and the population standard deviation is unknown, the value of the test statistic is calculated as __________.
tdf=x−−μo / s/√n
