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probability statistics
Using And Interpreting Statistics 3rd Edition Eric W. Corty - Solutions
If there are 28 students in a classroom and 18 of them are boys, what is the probability—if a student is picked at random—of selecting a boy?
Jong-Il was feeling depressed and anxious. His therapist gave him a depression test (M=10, s = 3, higher scores mean more depression)and an anxiety inventory (M = 80, s = 25, higher scores mean more anxiety). His score was a 15 on the depression test and a 110 on the anxiety inventory. Is Jong-Il
If z = 1.45, s = 3.33, and M = 12.75, what is X?
If X = 17.34, s = 5.45, and M = 24.88, what is z?
___ is a very important number in statistics.
If 45% of the scores fall in a certain section of the normal distribution, then p = ___ that a case selected at random from the population would have a score that falls in that section.
If someone is picked at random, what is the probability that her IQ will be 123 or higher? (Use a mean of 100 and a standard deviation of 15.)
What are the z scores that mark the middle 34% of scores?
If a researcher picked one date at random out of a year, what is the probability of it not being a Monday?
If a researcher picked one date at random out of a year, what is the probability of it being a Monday?
If the z scores that mark off the middle 60% of scores are ±.84, what are the z scores that mark off the extreme 40% of scores?
What’s the smallest possible probability for an outcome? The largest?
What is the definition of probability?
What is the percentile rank associated with a z score of −0.45?
If a person’s score, as a percentile rank, is 80, what is her z score?
What is the percentile rank for a score at the midpoint of a set of normally distributed scores?
What is a percentile rank?
What percentage of area in a normal distribution falls from the mean to a z score of −0.85?
What percentage of area in a normal distribution falls at or above a z score of 2.67?
What percentage of area in a normal distribution falls at or above a z score of −1.33?
What do numbers 34, 14, and 2 represent in a normal curve?
What measure of central tendency is the midpoint of a normal distribution?
Describe the shape of a normal distribution.
Another student’s GPA, expressed as a z score, is −2.30. What is his GPA?
The average GPA in a class is 2.75 with a standard deviation of 0.40.One student has a GPA of 3.20. Express this GPA as a z score?
If a z score is positive, what does that mean?
What is the sum of all z scores in a data set?
In what units do z scores express raw scores?
A meteorologist measured the temperature every 2 hours for a day in January and for a day in June. Here are the temperatures, in degrees Fahrenheit, for the January day: 23, 22, 21, 21, 23, 27, 28, 31, 32, 32, 30, and 26. The June temperatures were: 56, 56, 59, 62, 64, 67, 73, 75, 77, 76, 75, and
A researcher takes two samples, one with N = 10 and the other with N = 100, from the same population.a. Which sample, N = 10 or N = 100, will have to correct s 2less in order to approximate the population variance?b. Why is it sensible that Equation 3.6 works this way?
Select the appropriate measure of central tendency for each scenario:a. A researcher obtains a sample of men who have been married for 7 years and asks them to rate their levels of marital happiness on an ordinal scale that ranges from −7 (extremely unhappy) to +7 (extremely happy).b. An
A researcher has a set of positive numbers. No numbers are duplicates. The mean is greater than the median. Which of the following statements is true?a. It is likely that more of the numbers are greater than the mean than are less than the mean.b. It is likely that more of the numbers are less than
A teacher has a set of 200 numbers, where the mean is dramatically greater than the median. What does this suggest about the shape of the distribution?a. The distribution is probably normal.b. The distribution is probably bimodal.c. The distribution is probably flat.d. The distribution is probably
A librarian measured the number of pages in five books. No two had the same number of pages. Here are the results from four of the books: 150, 100, 210, and 330. Using the counting method, he calculated the median for all five books as 150. In the list below, what is the largest value possible for
Calculate s for these data, which have a mean of 3.30: 1.4, 2.2, 4.5, 4.1, and 4.3.
Calculate s for these data, which have a mean of 37.20: 24, 36, 42, 50, and 34.
If s 2 = 256.38, what is s?
If s 2 = 6.55, what is s?
An interval-level measure was obtained on a sample of four cases.Their raw scores were 21, 18, 12, and 9. Calculate s 2.
A nurse practitioner took a sample of five people from the population of people with high blood pressure and measured their systolic blood pressures as 140, 144, 148, 156, and 162 with a mean of 150.00. Calculate s 2.
A clinical psychologist took a sample of four people from the population of people with anxiety disorders and gave them an interval-level anxiety scale. Their scores were 57, 60, 67, and 68 with a mean of 63.00. Calculate s 2.
Given this data set (12, 9, 15, 13, and 11) with a mean of 12.00, find the following: (a) N, (b) Σ(X – M), (c) Σ(X – M)2.
A researcher obtained a sample from a population and measured an interval-level variable on each case. Here are the values he obtained:47, 53, 67, 45, and 38. He found M = 50.00. Find the following: (a)N, (b) Σ(X – M), (c) Σ(X – M)2.
a. Find the range for the data in Exercise 3.41.b. Which is a better measure of variability to report, the range or the interquartile range? Why?
Here is a listing, to the nearest million dollars, of the total payrolls for the 30 Major League baseball teams in 2009.a. Calculate the range.b. Which is a better measure of variability to report, the range or the interquartile range? Why?
Find the median and the mode for the following data: 30, 30, 32, 33, 35, 35, 38, 41, 42, 43, 45, 45, 48, 49, 50, 50, 50, 51, 52, 53, 53, 53, 53, 53, 53, 55, 55, 58, 59, 61, 62, 62, 64, 65, 66, 66, 67, 68, 70, 71, 71, 72, 72, 73, 73, 75, 76, 78, 79, and 80.
Find the median and the mode for the following data: 65, 66, 66, 70, 71, 72, 72, 72, 78, 83, 85, 86, 87, 87, 88, 88, 92, 93, 95, 95, 99, 100, 102, 102, 102, 102, 102, 103, 104, 108, 111, 113, 118, 119, 119, 119, 121, 121, 122, 128, 130, 131, 134, 136, 138, 139, and 145.
Given the following interval-level numbers, calculate the mean:0.13, 0.28, 0.42, 0.36, and 0.26.
Given the following ratio-level numbers, calculate the mean: 80, 88, 76, 65, 59, and 77.
An educational psychologist was teaching a graduate seminar with seven students. He was curious to know if the amount of sleep had an impact on performance. On the first exam, he asked how many hours the students had slept the night before. Here are the data he obtained: 8, 9, 7, 6, 8, 4, and 7.
A cardiologist wanted to measure the increase in heart rate in response to pain. She directed healthy volunteers to immerse their dominant hands into a bucket of ice water for 1 minute. Here are the increases in heart rate for her participants: 20, 23, 25, 19, 28, and 24.
A cognitive psychologist at a state university noted whether her research participants had been raised in a non–English-speaking household (0), an English-only–speaking household (1), or a multilingual, including English, household (2). Here are her data: 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
An industrial/organizational psychologist measured the number of errors seven research participants made in a driving simulator while talking on their cell phones. Here are her data: 12, 6, 5, 4, 4, 3, and 1.
If s for one set of data is 12.98 and it is 18.54 for a second set of data, then the first set of data has _____ variability than the second.
The first step in calculating a sample variance is to calculate a _____ for each case.
Sample values of variance and standard deviation are _____, so they are better approximations of the _____ values.
If the standard deviation is small, then the scores fall relatively close to the _____.
The average deviation score is not useful as a measure of variability because the _____ of the deviation scores is always _____.
If scores are _____ clustered around the mean, then there is less variability in that set of scores.
The information used from each case, in calculating variance and standard deviation, is its _____ score.
The variance and standard deviation, unlike the range and the interquartile range, use information from all of the _____.
The _____ is the square root of the _____ and tells the average distance by which the raw scores deviate from the mean.
The interquartile range can be used as a measure of _____ as well as variability.
If the interquartile range for student A’s grades is wider than it is for student B’s grades, then student A has _____ variability in his or her grades.
If the top 25% of scores and the bottom 25% of scores are trimmed off the range, it is called the _____.
The range is/is not influenced by outliers.
The range, interquartile range, variance, and standard deviation can only be used with variables measured at the _____ or _____ level.
If one has nominal data, one should use a _____ as the measure of central tendency.
If one has interval or ratio data and the data set is multimodal, one should use _____ as the measure of central tendency.
If one has interval or ratio data and the data set is skewed, one should use a _____ as the measure of central tendency.
If one has interval or ratio data, the first choice for a measure of central tendency to calculate should be a _____.
The formula for a _____ is X – M.
The three measures of central tendency covered in this chapter are _____, _____, and _____.
The two dimensions used in this chapter to summarize a set of data are measures of _____ and _____.
The American Association of Organic Apple Growers took a sample of five family farms and determined how large, in acres, the orchards were. The results were 23, 8, 22, 10, and 32 with a mean of 19.00.Calculate (a) sample variance and (b) sample standard deviation for the size, in acres, of the five
A clinical psychologist took 12 people who were diagnosed with depression and gave them an interval-level depression scale. On this scale, scores above 70 are considered to be indicative of clinical depression. Here are the 12 scores: 65, 81, 66, 83, 70, 70, 72, 60, 78, 78, 79, and 84. What is the
What is an advantage of the variance and standard deviation over the range and interquartile range as measures of variability?
What is an advantage of the interquartile range as a measure of variability?
What is a disadvantage of the range as a measure of variability?
What does it mean when one set of scores has more variability than another set?
A sensory psychologist measured whether taste buds were primarily sensitive to (1) bitter, (2) salty, (3) savory, (4) sour, or (5) sweet.Here are the data for her sample of taste buds: 1, 2, 3, 4, 5, 5, 5, 3, 2, 3, 4, 5, 1, 5, 4, and 5.
A neuroscientist measured how often a sample of neurons fired during a specified period of time. The 10 values were 1, 11, 10, 10, 2, 2, 3, 10, 9, and 2.
A school psychologist measured the IQs of seven children as 94, 100, 110, 112, 100, 98, and 100.
What impact does a skewed data set have on the mean?
Which measure of central tendency can be used (a) for nominal-level data? (b) For ordinal-level data? (c) For interval- or ratio-level data?
List the three measures of central tendency.
Make a stem-and-leaf display for these data. Use an interval width of 5.120, 122, 123, 123, 124, 125, 126, 125, 126, 130, 134, 135, 135, 138, 147
Diane wears a digital watch that reports the time to the nearest minute. At 10:16 A.M., by her watch, she left her office. She returned at 10:21 A.M. To the nearest minute, what is the shortest amount of time that she was out of her office? What is the longest?
If a researcher has a grouped frequency distribution for a continuous variable and there are five people in the interval ranging from 50 to 54, what X values should he assign them if he wants to assign values?a. He should randomly select values from 50 to 54.b. He should randomly select values from
If the real limits and apparent limits for an interval are the same, then the variable is:a. continuous.b. discrete.c. interval.d. ratio.e. Real and apparent limits are never the same.
Make a stem-and-leaf display for these data and comment on the shape of the distribution: 8, 9, 13, 13, 16, 21, 22, 24, 25, 25, 29, 33, 33, 45, 48, 55, 58, 61, 63, 64, 66, 66, 69, 71, 83, 92, 93, and 95.
Make a stem-and-leaf display for these data and comment on the shape of the distribution: 11, 12, 21, 23, 27, 27, 29, 30, 30, 33, 34, 35, 39, 43, 45, 47, 53, 53, 67, 75, 84, and 96.
A developmental psychologist observes how children interact with their parents and classifies the children’s attachment as secure, avoidant, resistant, or disorganized. He classifies 33 children as securely attached, 17 as avoidant, 13 as resistant, and 21 as disorganized. Graph this frequency
For each scenario, tell what the real limits of the number/interval are:a. If a person’s temperature is reported as 100.3 (and not 100.2 or 100.4), what is the interval within which the person’s temperature really falls?b. If a family has 7 children, not 6 or 8, what is the interval within
Below are sets of consecutive numbers, or intervals, from frequency distributions for continuous variables. For the second number (or interval) in each set, the one in bold, identify the real lower limit, real upper limit, interval width, and midpoint.a. 27–30; 31–34; 35–38b. 10–20;
For each variable, decide if it is continuous or discrete:a. The depth, in inches, a person can drive a 3-inch nail with one hammer blowb. The number of students in a classroom who are absent for at least one day during the month of Februaryc. The total number of days that students in a classroom
For each variable, decide if it is discrete or continuous:a. The number of cases of flu diagnosed at a college in a given semesterb. The weight, in grams, of a rat’s hypothalamusc. The number of teachers, including substitutes, in a school district who are certified to teach high school mathd.
A professor of education was curious about students’ expectations of academic success. She obtained a sample of college students at the start of their college careers and asked them what they thought their GPAs would be for the first semester. Below are the data she obtained. Make a grouped
In a stem-and-leaf display for 21, 21, 24, 25, 28, 30, 31, 34, and 39, the numbers 2 and 3 would be the _____s and 0, 1, 4, 5, 8, and 9 would be the _____s.
A stem-and-leaf display summarizes a data set like a _____ frequency distribution.
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