Applied Statistical Methods 1

A local corporation was interested in the purchasing habits of Wake County residents.Specifically one of the things they were interested in was the proportions of residents that did a major home improvement project in the last year.The corporation used a list of all households to take a simple random sample of households.The researcher then visited each of the sampled homes and found that 21 of 100 homes had completed a major home improvement project. Which of the following are true? Select one or more:

Online website surveys such as “quick votes” Select one or more:

The state Department of Public Instruction (DPI) would like to sample high school mathematics teachers to complete a survey on teaching methods. Among high school teachers some are National Board Certified (NBC) Teachers and some are not. A researcher compiled a list of all high school mathematics teachers in the state and divide the list into NBC teachers and non-NBC teachers. She then numbered these two lists and use a random number generator to pick 50 NBC teachers and 50 non-NBC teachers. This sample is best described as Select one:

A researcher wants to find out how college students feel about the Social Security system. Which of the following unbiased methods could the researcher use? Select one or more:

In a recent survey several individuals could not be found even after three attempts to contact them. This is an example of: Select one:

The student government at the University of Missouri conducted a survey of the university's students. Three hundred (300) of the 26,000 students were contacted and asked if there was a need for an additional parking garage on campus. Of the 300 students contacted 23% said an additional garage was needed. Which of the following would possibly be an example of undercoverage? Select one:

Does daily exposure to bright light make subjects more alert? A study was conducted in which the daily habits of 30 college students were documented, focusing on how much time they spent in brightly lit rooms or outside on sunny days.After a week, the subjects were given a computer-based alertness test on which they receive a score on a 0 to 100 point scale.Their scores were compared with how much time they spent in brightly lit places that week. Select one or more:

About 870 men took part in a study to study the effectiveness of a hormone therapy. Half of the men were selected randomly to come in and receive the hormone therapy while the other half were told to stay home and thus did not receive the therapy. After about a year, blood tests were conducted on each subject by a lab technician who was aware of which group (treatment or those given nothing) the blood samples originated from. In presenting the results of the experiment, the authors reported that the men in the treatment group had experienced a statistically significant increase in HDL (the so-called "good" cholesterol) and a statistically significant reduction in LDL (the so-called "bad" cholesterol) when compared with the control group. Select one or more:

A researcher wants to test how diets A and B affect the weight loss of rabbits. She has 20 rabbits to use, but all of the rabbits are different sizes, which might affect how much weight they lose. The researcher decides to group the four smallest rabbits in one group, the next four smallest rabbits in another group, etc., until the final group has the four largest rabbits. Then, from each group she randomly selects two rabbits to have diet A, and the remaining rabbits in the groups have diet B. Select one or more:

An experiment that claimed to show that meditation reduces anxiety proceeded as follows. The experimenter interviewed the subjects and rated their anxiety. The subjects were then randomly assigned to two groups. The experimenter taught one group how to meditate, and they meditated daily for a month. The other group was simply told to relax more. At the end of the month, the experimenter interviewed all the subjects again and rated their anxiety levels. The meditation group had less anxiety. This study was criticized for not being blinded. What does ‘not blinded’ mean? Select one:

In research studies the placebo effect Select one:

The school committee of a small town surveys every family in the town and records X = {the number of children in each household}. Based on this data, they calculate E(X) = 2.2. Select the best interpretation of the expected value in this context. Select one:

Use the following for questions 13 - 15 Let X be a continuous random variable with distribution: f(x) = (1/10) + (x/5) for 1 <= x <= 3 What is the cumulative distribution function of X? Select one:

Use the following for questions 2 to 4. Let X be a continuous random variable with distribution: f(x) = (1/10) + (x/5) for 1 <= x <= 3 Calculate P(1.7 < X < 2.2). Round your answer to 3 decimal places and do not include any symbols other than a decimal point. Answer: [blank_start]0.245[blank_end]

Use the following for questions 2 to 4. Let X be a continuous random variable with distribution: f(x) = (1/10) + (x/5) for 1 <= x <= 3 Calculate the expected value of X. Round your answer to 3 decimal places and do not include any symbols other than a decimal point or negative sign, if necessary. Answer: [blank_start]2.133[blank_end]

Suppose 20% of all purchases at a particular online store are made with PayPal. Let X = the number of purchases made at this store with PayPal out of 15 randomly selected purchases. [Note: the fact that the purchases were randomly selected implies they will be independent.] What is the probability that exactly 4 purchases are made with PayPal at this store? Give your answer to 4 decimal places. Do not include symbols other than a decimal point. Answer: [blank_start]0.1876[blank_end]

Suppose 20% of all purchases at a particular online store are made with PayPal. Let X = the number of purchases made at this store with PayPal out of 15 randomly selected purchases. [Note: the fact that the purchases were randomly selected implies they will be independent.] Consider the previous problem. How many purchases at this store would we expect to be made with PayPal? Answer: [blank_start]3[blank_end]

After taking an aptitude test, the computer told Bob that he had a z-score of -1.08. If scores on the aptitude test are normally distributed, which of the following statements can Bob conclude from his score? Select one or more:

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 15. What proportion of children have MDI of at least 88? Select one:

A state administered standardized reading exam is given to eighth grade students. The scores on this exam for all students statewide have a normal distribution with a mean of 502 and a standard deviation of 43. A local Junior High principal has decided to give an award to any student who scores in the top 10% of statewide scores. How high should a student score be to win this award? Report your answer to 2 decimal places. Answer: [blank_start]557.11[blank_end]

A continuous random variable X is said to have a uniform distribution if the pdf of X is: f(x) = 1 / (b-a) for a < X < b Show that f(x) is a valid probability distribution and use the definition of expected value to derive a form for the mean of X [blank_start]E(X) = (b+a)/2[blank_end]

An instructor in a college class recently gave an exam that was worth a total of 100 points. The instructor inadvertently made the exam harder than he had intended. The scores were very symmetric, but the average score for his students was 54 and the standard deviation of the scores was 4 points. The instructor is considering 2 different strategies for rescaling the exam results: Method 1: Add 20 points to everyone's score. Method 2: Multiply everyone's score by 1.5. Select one:

A large multinational company knows that the average age of their employees is 34 years. They also know that the standard deviation of the ages of these employees is 8 years. We know that the population of employee ages will have a right skewed distribution. A manager from human resources is going to randomly select a sample of 100. Which of the following is true? Select all that apply. Select one or more:

From census data it is known that the average income of households in Wake County is $58,500. It is also known that the distribution of household income in Wake County is strongly skewed to the right with a standard deviation of $14,000. A researcher is going to randomly select a sample of 5 households from Wake County. Which of the following is true? Select all that apply. Select one or more:

The Mental Development Index (MDI) of the Bayley Scales of Infant Development is a standardized measure used in longitudinal follow-up of high-risk infants. The scores on the MDI have approximately a normal distribution with a mean of 100 and standard deviation of 16. We are going to randomly select 64 children and average their MDI scores. What is the probability that the average is under 105? Give your answer to 4 decimal places. Answer: [blank_start]0.9938[blank_end]

In engineering and product design, it is important to consider the weights of people so that airplanes or elevators aren't overloaded. Based on data from the National Health Survey, we can assume the weight of adult males in the US has a mean weight of 177 pounds and standard deviation of 32 pounds. We randomly select 50 adult males. What is the probability that the average weight of these 50 adult males is over 190 pounds? Give your answer to 4 decimal places. Answer: [blank_start]0.0021[blank_end]

A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X = the proportion of the time the drive-through facility is in use and let Y = the proportion of the time the walk-in facility is in use. Suppose that the joint distribution of X and Y is f(x,y)=(2/3)(x+2y) for 0<x<1 and 0<y<1 What proportion of the time is the drive-through facility expected to be in use?

A fast-food restaurant operates both a drive-through facility and a walk-in facility. On a randomly selected day, let X = the proportion of the time the drive-through facility is in use and let Y = the proportion of the time the walk-in facility is in use. Suppose that the joint distribution of X and Y is f(x,y)=(2/3)(x+2y) for 0<x<1 and 0<y<1 What is the probability that the drive-through facility and the walk-in facility are each in use less than half of the time? Select one:

Consider three independent random variables--X, Y, and Z, such that E(X) = 6, V(X) = 2 E(Y) = 10, V(Y) = 5 E(Z) = 3, V(Z) = 1 Calculate E(2X + Y - 3Z). Select one:

Consider three independent random variables--X, Y, and Z, such that E(X) = 6, V(X) = 2 E(Y) = 10, V(Y) = 5 E(Z) = 3, V(Z) = 1 Calculate V(2X + Y - 3Z). Select one:

Suppose that in a certain examination procedure, candidates must take two tests. Let X1 measure the score of a candidate on test 1 and X2 measure the score of a candidate on test 2. Further, suppose that scores on test 1 are distributed with a mean of 18 and a variance of 24 points, while scores on test 2 are distributed with a mean of 30 and a variance of 60 points. An examination board wishes to calculate a final score for each candidate that is a weighted average these two test scores using the following formula: Y = (2/3)*X1 + (1/3)*X2 Based on this information, which of the following is true? Select one or more:

Which of the following are true? Select one or more:

df=10, 90% confidence [blank_start]Answer 1[blank_end] df=16, 80% confidence [blank_start]Answer 2[blank_end] df=2, 99% confidence [blank_start]Answer 3[blank_end] df=4, 98% confidence [blank_start]Answer 4[blank_end]

The director of student health at a small high school is studying how many calories students at her high school consume in a day. She asks the first 40 students who come to the health room how many calories they consume in a 24 hour period and records the results. From the sample she found the average number of calories consumed was 1851 and that the standard deviation was 350. However before she finds the confidence interval for how many calories students consume in one day she goes to the statistics teacher for advice. What should the statistics teacher's advice be? Select one or more:

We would like to create a confidence interval. Which of the following would produce the smallest margin of error? Select one:

In creating confidence intervals for the mean with 95% confidence we have about 5% of the possible intervals that will miss the true population parameter. Why do some of the intervals miss the true parameter? Select one

We should be wary of a poll that has a high non-response rate because Select one:

An administrator with the Missouri State Board of Education would like to determine the proportion of graduating seniors in the state that have been accepted into college for the next year. They would like to take a random sample of at least 1000 subjects. What is the parameter of interest in this situation? Select one:

A crop scientist is conducting research with a drought resistant corn hybrid. She is interested in determining if increasing the spacing between these plants will increase plant height. She prepares 20 single acre plots and randomly assigns 10 to have normal spacing while the other 10 are planted with an expanded spacing. The resulting average height for each group of 10 plots was recorded. Select all that apply. Select one or more:

Let X be a continuous random variable with Cumulative Density Function (CDF) F(x)=1- 1/[(x+1)^(2)] for x > 0. What is P(1 < X < 2)? Select one:

A forestry researcher wants to estimate the average height of trees in a forest near Atlanta, Georgia. She takes a random sample of 18 trees from this forest. The researcher found that the average height was 4.8 meters with a standard deviation of 0.55 meters. Assume that the distribution of the heights of these trees is normal. For this sample what is the margin of error for her 99% confidence interval? Give your answer to 3 decimal places. Answer: [blank_start]0.376[blank_end]

A survey of undergraduates at NCSU asked a random sample of 80 students about the amount they had spent on textbooks (in dollars) during the current term. The 95% confidence interval created from this data was $375 ± $35. Which of the following statements are true?

It is reported that 30% of all pipework failures in chemical plants are caused by operator error; suppose this is the true probability p of a pipework failure being caused by operator error. Calculate the probability that 6 out of a random sample of 10 pipework failures would be caused by operator error. Report your answer to 4 decimal places. Answer: [blank_start]0.0368[blank_end]

An elementary school teacher wanted to determine if one song about a certain history topic would improve students' understanding of the topic over another song. A teacher had 24 students in her class, and she randomly assigned 12 students to learn the first song, and 12 students to learn the second song. The next day the teacher gave the students a test on the history topic. This study would best be described as Select one: