Stats Test 1-7
The sum of the squared deviation scores is SS = 60 for a sample of n = 5 scores. What is the variance for this sample?
60/4 = 15
If a coin is balanced so that p(Heads) = p(Tails) = 1/2, then which of the following outcomes is more unlikely to occur?
75 heads in 100 tosses
The binomial distribution for p = 0.20 and n = 100 has a standard deviation of 𝜎 = 4.
True
The following data represent salaries, in thousands of dollars, for employees of a small company. Notice the data have been sorted in increasing order. (a) Look at the last data value. Does it appear to be an outlier? Could this be the owner's salary? (b) Does this histogram reflect the salary distribution of most of the employees better than the histogram in part (a)?
Yes, it is an outlier and it is likely the owner's salary. Yes
In a normal distribution, what z-score value separates the highest 40% of the scores from the rest of the distribution?
Z=1.28
During the winter in New York, the lower the temperature drops, the higher the demand for energy. This is an example of
a negative relationship
In a normal shaped distribution, ______.
the scores pile up in the middle and taper off symmetrically to both sides
Which set of scores has the smallest standard deviation?
145, 143, 145, 147
A population of N = 10 scores has 𝜇 = 50 and 𝜎 = 5. What is the population variance?
25
A normal distribution has a mean of 𝜇 = 24 with 𝜎 = 3. What score is needed to place in the top 14% of the distribution?
27.24
For a sample of n = 100, what is the standard deviation of the binomial distribution with p = .20 and q = .80?
4
A vertical like is drawn through a normal distribution at z = +0.25. The line separates the distribution into two sections. What proportion of the distribution is in the smaller section?
40.13%
For the following distribution, what is the width of each class interval? X f 20 - 25 2 15 - 19 5 10 - 14 4 5 - 9 1
5
The Customer Service Center in a large New York department store has determined that the amount of time spent with a customer about a complaint is normally distributed, with a mean of 10.3 minutes and a standard deviation of 2.4 minutes. What is the probability that for a randomly chosen customer with a complaint, the amount of time spent resolving the complaint will be as follows.
(a) less than 10 minutes 4483 between 8 and 15 minutes 8065
Scores from a statistics exam are reported as deviation scores. Which of the following deviation scores indicates a higher position in the class distribution?
+8
Which of the following Pearson correlations shows the greatest strength or consistency of relationship?
-0.90
In a population with 𝜇 = 50, what deviation score would have a score of X = 45?
-5
What proportion of a normal distribution falls between z = −1.16 and z = +1.16?
.6230 0R .3770
Express Courier Service has found that the delivery time for packages is normally distributed, with mean 15 hours and standard deviation 2 hours. For a package selected at random, what is the probability that it will be delivered in 18 hours or less?
.9332
A normal distribution has a mean of 𝜇 = 40 with 𝜎 = 4. What is the probability of sampling an individual with a score greater than 46?
0.0668
What proportion of a normal distribution is located in the tail beyond a z-score of z = 1.50?
0.0668
What proportion of a normal distribution corresponds to z-scores greater than +1.04?
0.1492
A vertical line is drawn through a normal distribution at z = −0.50. What proportion of the distribution is located between the mean and the line?
0.1915
What is the probability of randomly selecting a z-score greater than z = 0.25 from a normal distribution?
0.4013
A data set with whole numbers has a low value of 20 and a high value of 96.Find the class width for a frequency table with seven classes. Find the class limits for a frequency table with seven classes
11 Lower class limit − Upper class limit First class 20 − 30 Second class 31 − 41 Third class 42 − 52 Fourth class 53 − 63 Fifth class 64 − 74 Sixth class 75 − 85 Seventh class 86 − 96
A binomial distribution has a mean of 𝜇 = 12 for a sample of n = 60. What is the value of p?
12/60= .2
Professor Cramer determines a final grade based on attendance, two papers, three major tests, and a final exam. Each of these activities has a total of 100 possible points. However, the activities carry different weights. Attendance is worth 7%, each paper is worth 9%, each test is worth 12%, and the final is worth 39%. (a) What is the average for a student with 89 on attendance, 96 on the first paper, 69 on the second paper, 82 on test 1, 69 on test 2, 84 on test 3, and 94 on the final exam?
85.94
A distribution is normal and has 𝜇 = 90 and 𝜎 = 10. What is the 64th percentile?
93.6
A new muscle relaxant is available. Researchers from the firm developing the relaxant have done studies that indicate that the time lapse between administration of the drug and beginning effects of the drug is normally distributed, with mean 𝜇 = 38 minutes and standard deviation 𝜎 = 5 minutes. (a) The drug is administered to one patient selected at random. What is the probability that the time it takes to go into effect is 35 minutes or less? (b) The drug is administered to a random sample of 10 patients. What is the probability that the average time before it is effective for all 10 patients is 35 minutes or less? (c) Comment on the differences of the results in parts (a) and (b).
A- .2742 B- .0289 C- The probability in part (b) is smaller than the probability in part (a) because the standard deviation is smaller for the x distribution.
State Farm Insurance studies show that in Colorado, 50% of the auto insurance claims submitted for property damage were submitted by males under 25 years of age. Suppose 12 property damage claims involving automobiles are selected at random. (a) What is the probability that five or more claims are made by males under age 25? (b) What is the expected number of claims made by males under age 25? What is the standard deviation of the r-probability distribution?
A- .806 B- 𝜇6 𝜎1.73
Consumer Reports rated airlines and found that 79% of the flights involved in the study arrived on time (i.e., within 15 minutes of scheduled arrival time). Assuming that the on-time arrival rate is representative of the entire commercial airline industry, consider a random sample of 203 flights. What is the expected number that will arrive on time? What is the standard deviation of this distribution?
A- 160.37 B- 5.8
Consider sample data with x = 20 and s = 4. (a) Compute the coefficient of variation. (b) Compute a 75% Chebyshev interval around the sample mean.
A- 20% B- Lower Limit 12 Upper Limit 28
Categorize the type of sampling (simple random, stratified, systematic, cluster, or convenience) used in each of the following situations. (a) To conduct a pre election opinion poll on a proposed amendment to the state constitution, a random sample of 10 telephone prefixes (first three digits of the phone number) was selected, and all households from the phone prefixes selected were called. (b) To conduct a study on depression among the elderly, a sample of 30 patients in one nursing home was used. (c) To maintain quality control in a brewery, every 20th bottle of beer coming off the production line was opened and tested. (d) Subscribers to a new smart phone app that streams songs were assigned numbers. Then a sample of 30 subscribers was selected by using a random-number table. The subscribers in the sample were invited to rate the process for selecting the songs in the playlist. (e) To judge the appeal of a proposed television sitcom, a random sample of 10 people from each of three different age categories was selected and those chosen were asked to rate a pilot show.
A- Cluster sample B- convenience sample C- Systematic Sample D- simple random sample E- stratified sample
For a binomial probability distribution, it is unusual for the number of successes to be less than 𝜇 − 2.5𝜎 or greater than 𝜇 + 2.5𝜎 (a) For a binomial experiment with 10 trials for which the probability of success on a single trial is 0.2, is it unusual to have more than five successes? Explain. (b) If you were simply guessing on a multiple-choice exam consisting of 10 questions with 5 possible responses for each question, would you be likely to get more than half of the questions correct? Explain.
A- No. The upper limit of successes that would be deemed to be usual is 6, so more than 5 successes would not be unusual. B- No. P(x > 5) is large, so it would be unlikely to get more than half of the questions correct.
Which technique for gathering data (observational study or experiment) do you think was used in the following studies? Explain your answer. (a) The U.S. Census Bureau tracks population age. In 1900, the percentage of the population that was 19 years old or younger was 44.4%. In 1930, the percentage was 38.8%; in 1970, the percentage was 37.9%; and in 2000, the percentage in the age group was down to 28.5% (b) After receiving the same lessons, a class of 100 students was randomly divided into two groups of 50 each. One group was given a multiple-choice exam covering the material in the lessons. The other group was given an essay exam. The average test scores for the two groups were then compared.
A- This is an observational study because observations and measurements of individuals are conducted in a way that doesn't change the response or the variable being measured. B-This is an experiment because a treatment was deliberately imposed on the individuals in order to observe a possible change in the response or variable being measured.
Consumer Banker Association released a report showing the lengths of automobile leases for new automobiles. The results are as follows. (a) Use the midpoint of each class, and call the midpoint of the last class 66.5 months, for purposes of computing the expected lease term. Also find the standard deviation of the distribution.
A- expected lease term 36.85 months
"Radon: The Problem No One Wants to Face" is the title of an article appearing in Consumer Reports. Radon is a gas emitted from the ground that can collect in houses and buildings. At certain levels it can cause lung cancer. Radon concentrations are measured in picocuries per liter (pCi/L). A radon level of 4 pCi/L is considered "acceptable." Radon levels in a house vary from week to week. In one house, a sample of 8 weeks had the following readings for radon level (in pCi/L). (a) Find the mean, median, and mode. (b) Find the sample standard deviation, coefficient of variation, and range. (c) Based on the data, would you recommend radon mitigation in this house? Explain.
A- median- 4.1 mode- 1.9 B- s= 2.473 range= 6.6 C- Yes, since the average and median values are both over "acceptable" ranges.
You are conducting a study of students doing work-study jobs on your campus. Among the questions on the survey instrument are the following. A. How many hours are you scheduled to work each week? Answer to the nearest hour.B. How applicable is this work experience to your future employment goals? Respond using the following scale: 1= not at all, 2 = somewhat, 3 = very (a) Suppose you take random samples from the following groups: freshmen, sophomores, juniors, and seniors. What kind of sampling technique are you using (simple random, stratified, systematic, cluster, multistage, convenience)? (b) Describe the individuals of this study (c) What is the variable for question A? (D) Classify the variable as qualitative or quantitative. (e) What is the level of measurement? (f) What is the variable for question B? (g) Classify the variable as qualitative or quantitative. (h) What is the level of measurement? (I) Is the proportion of responses "3 = very" to question B a statistic or a parameter? (j) Suppose only 40% of the students you selected for the sample respond. What is the nonresponse rate? (K) Do you think the nonresponse rate might introduce bias into the study? Explain. (L) Would it be appropriate to generalize the results of your study to all work-study students in the nation? Explain.
A- stratified Sample B- Students on your campus with work study jobs C- hours scheduled D- quantitative E- Ratio F- Rating of applicability of work experience to future employment G- qualitative H- ordinal I- Statistic J- 60% K- Yes, the people choosing not to respond may have some characteristics that would bias the study. L- No, the sample frame is restricted to one campus.
Let x be a random variable representing percentage change in neighborhood population in the past few years, and let y be a random variable representing crime rate (crimes per 1000 population). A random sample of six Denver neighborhoods gave the following information. x 26 1 11 17 7 6 y 176 35 132 127 69 53 Σx = 68; Σy = 592; Σx2 = 1,172; Σy2 = 73,324; Σxy = 9,023 (a) Find x, y, b, and the equation of the least-squares line. (b) Find the sample correlation coefficient r and the coefficient of determination. (c) What percentage of variation in y is explained by the least-squares model? (d) For a neighborhood with x = 23% change in population in the past few years, predict the change in the crime rate (per 1000 residents).
A- x= 11.33 y= 98.67 b= 5.765 ŷ= 33.331 + 5.765 x B- r =0.946 r2 =0.895 C- 89.5% D- 165.9 crimes per 1000 residents
Bighorn sheep are beautiful wild animals found throughout the western United States. Let x be the age of a bighorn sheep (in years), and let y be the mortality rate (percent that die) for this age group. For example, x = 1, y = 14 means that 14% of the bighorn sheep between 1 and 2 years old died. A random sample of Arizona bighorn sheep gave the following information: x 1 2 3 4 5 y 14.6 19.7 14.4 19.6 20.0 Σx = 15; Σy = 88.3; Σx2 = 55; Σy2 = 1,592.77; Σxy = 275.6 (a) Find x, y, b, and the equation of the least-squares line. (b) Find the sample correlation coefficient r and the coefficient of determination r2 (c) What percentage of variation in y is explained by the least-squares model?
A- x= 3 y= 17.66 b= 1.07 ŷ= 14.45 + 1.07 x B- r =0.586 r2 =0.343 C- 34.3 %
Which of the following pairs of variables should produce a correlation near zero?
IQ and weight for a group of third-grade students
When using the least-squares line for prediction, are results more reliable for extrapolation or interpolation?
Interpolation, because we are predicting from data in the range used to create the least-squares line.
Which of the following is not a continuous variable?
Number of children in a family
Ranking a group of cities in terms of "quality of life" would be an example of measurement on a(n) _____ scale of measurement.
Ordinal
Using letter grades (A, B, C, D, and E) to classify student performance on an exam is an example of measurement on a(n) _______ scale of measurement.
Ordinal
Given that x is a normal variable with mean 𝜇 = 45 and standard deviation 𝜎 = 6.7, find the following probabilities.
P(x ≤ 60).9875
What value is obtained if you add all the deviation scores for a population, then divide the sum by N?
Population standard deviation
For a population of N = 10 scores, you first measure the distance between each score and the mean, then square each distance and find the sum of the squared distances. At this point you have calculated _____.
SS
A Pearson correlation of r = +0.85 indicates that a graph of the data would show ___.
Slopes up and to the right
What are the requirements for a probability distribution?
The probability distribution has a probability assigned to each distinct value of the random variable. The sum of all the assigned probabilities must be .
List the criteria for a binomial experiment
The probability of success on each trial is constant The trials are independent The trials have exactly two outcomes A fixed number of trials repeated under identical conditions
What does the random variable of a binomial experiment measure
The random variable measures the number of successes in n trials.
A researcher is using an experiment to determine whether sugar consumption has any effect on the activity level of preschool children. For this study, the dependent variable is the activity level of the children.
True
A researcher records how much time each participant needs to solve a series of problems. This is an example of a continuous variable.
True
Determining the number of students in each psychology course would be an example of measurement on a ratio scale.
True
If other factors are held constant, both the mean and standard deviation for the binomial distribution increase as the sample size increases.
True
For these data, the Pearson correlation ______. X Y 2 4 5 2 3 5 2 5
cannot be determined
Many people say the civil justice system is overburdened. Many cases center on suits involving businesses. The following data are based on a Wall Street Journal report. Researchers conducted a study of lawsuits involving 1908 businesses ranked in the Fortune 1000 over a 20-year period. They found the following distribution of civil justice caseloads brought before the federal courts involving the businesses. Note: Contracts cases involve disputes over contracts between businesses. Which type of cases occur most frequently?
general torts
A negative value for a correlation indicates ______.
increases in X tend to be accompanied by decreases in Y
A positive value for a correlation indicates _____.
increases in X tend to be accompanied by increases in Y
The following data represent weights in kilograms of maize harvest from a random sample of 72 experimental plots on St. Vincent, an island in the Caribbean 7.8 9.1 9.5 10.0 10.2 10.5 11.1 11.5 11.7 11.8 12.2 12.2 12.5 13.1 13.5 13.7 13.7 14.0 14.4 14.5 14.6 15.2 15.5 16.0 16.0 16.1 16.5 17.2 17.8 18.2 19.0 19.1 19.3 19.8 20.0 20.2 20.3 20.5 20.9 21.1 21.4 21.8 22.0 22.0 22.4 22.5 22.5 22.8 22.8 23.1 23.1 23.2 23.7 23.8 23.8 23.8 23.8 24.0 24.1 24.1 24.5 24.5 24.9 25.1 25.2 25.5 26.1 26.4 26.5 26.7 27.1 29.5 (a) Compute the five-number summary Discuss the distribution. Does the lower half of the distribution show more data spread than the upper half?
min- 7.8 Q1- 13.5 Median- 19.2 Q3- 23.8 Max- 29.5 The lower half shows slightly more spread
Determining a person's age (in years) would involve measurement on a(n) _____ scale of measurement.
nominal
Which of the following is an example of a discrete variable?
number of brothers and/or sisters
Although research questions usually concern a _________, the actual research is typically conducted with a ________.
population, sample
For which of the following correlations would the data points be clustered most closely around a straight line?
r = −0.80
After measuring a set of individuals, a researcher finds that Bob's score is three times greater than Jane's score. These measurements must come from a(n) ________ scale.
ratio
In any normal distribution, what are the z-score boundaries for the middle 50% of the distribution?
z = ±0.67
A scatter plot shows a set of data points that are clustered close to a line that slopes down to the right. Which of the following values would be closest to the correlation for these data?
−0.80
A population of scores has 𝜇 = 50 and 𝜎 = 10. If 5 points are added to every score in the population, then the new mean and standard deviation would be _____.
𝜇 = 55 and 𝜎 = 10
