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theory of statistics

Questions and Answers of Theory of Statistics

Given a normal population distribution with μ = 71 and σ = 14,a. what is the probability of obtaining a sample mean greater than 76 if n = 44?b. what proportion of sample means can be expected to
Given a normal population distribution with μ = 62 and σ = 15,a. what is the probability of obtaining a sample mean less than 61 if n = 53?b. what proportion of sample means can be expected to
An assessment instrument on assertiveness has been standardized with a mean of 90 and a standard deviation of 20. A large manufacturing company administers the test to its sales force. If n = 64,
Given a normally shaped population distribution with μ = 88 and σ = 12, what is the probability that an obtained sample of size n = 36 will have a mean that isa. above 92?b. above 87?c. below 87?
Explain what is meant by the standard error of the mean. How is it related to sample size?What are the practical implications of this relationship?
The Wechsler IQ has a μ = 100 and a σ = 15.a. Compute σM for a sample size of n = 120.b. Compute σM for a sample size of n = 50.c. How is σM affected by sample size?
Why is it important to exercise caution when using a sample mean to make a prediction about the population mean?
Briefly discuss the characteristics outlined by the central limit theorem.
What is a sampling distribution and what is its purpose?
A normally shaped distribution has a μ = 34 and σ = 4. What raw scores are so extreme that they will be achieved by only 3% of the population?
A normally shaped distribution has a μ = 71 and σ = 6. What raw scores are so extreme that they will be achieved by only 9% of the population?
Given a normal distribution with a μ = 96 and σ = 12, what raw score separates the lower 56% of the distribution from the upper 44%?
Given a normal distribution with a μ = 40 and σ = 4, what raw score separates the upper 68% of the distribution from the lower 32%?
A normal distribution has a μ = 36 and σ = 3. What is the probability that a randomly selected score would fall between 28 and 32?
A normal distribution has a μ = 57 and σ = 8. What is the probability that a randomly selected score would fall between 59 and 71?
A normal distribution has a μ = 84 and σ = 6.a. What proportion of the population can be expected to obtain scores between 72 and 89?b. What is the proper notation for the above question and answer?
A normal distribution has a μ = 50 and σ = 5.a. What proportion of the population can be expected to obtain scores between 42 and 53?b. What is the proper notation for the above question and answer?
Given a normal distribution with a μ = 112 and σ = 10, what percentage of the population can be expected to scorea. lower than 100?b. higher than 90?
Given a normal distribution with a μ = 37 and σ = 4, what proportion of the population can be expected to scorea. greater than 40?b. greater than 25?c. less than 32?d. less than 39?
Given a normal distribution with a μ=82 and σ =8, determine the following proportions:a. p(X > 93)b. p(X > 72)c. p(X < 63)d. p(X < 104)
What z-score separates the lowest 25% of the normal distribution from the highest 75%?
What z-score separates the highest 35% of the normal distribution from the lowest 65%?
Locate the z-scores associated with the following:a. lowest 40% of the normal distributionb. highest 56% of the normal distributionc. highest 12.5% of the normal distribution
Locate the probabilities associated with the following:a. p(z > +1.25)b. p(z > −2.10)c. p(z < −1.87)d. p(z < +2.68)
The Table of the Normal Distribution Curve is made up of four columns. Briefly describe what each column contains.
Which score is higher: a Wechsler IQ score of 112 or an SAT score of 600? Explain.
A set of scores follows: 8, 7, 6, 5a. What is the z-score for a raw score of 5?b. What is the z-score for a raw score of 7?
A set of raw scores follows: 12, 11, 10, 9, 8, 7a. What is the z-score for a raw score of 9?b. What is the z-score for a raw score of 12?
A set of scores has a mean of 65.83 and a standard deviation of 5.41. Erica scored 1.12 standard deviations below the mean and Gianna scored 1.08 standard deviations above the mean.a. What was
A personality psychologist is developing a new personality inventory, which she calls FLEX, designed to measure resilience. The new assessment will be standardized with a mean of 70 and a standard
Students taking a college prep course take a practice SAT test. The mean for the class was 108 with a standard deviation of 11. Using the same μ and σ of the standardized SAT test, the course tutor
A distribution of scores has a μ = 75 and a σ = 8. What is the z-score for the following X values?a. 95b. 63c. 75d. 82
There were four exams in Liam’s sociology class. He scored 68 on the first exam, 72 on the second, 80 on the third, and 65 on the fourth. The means and standard deviations for the exams are listed
The average weight of a popular brand of cookies is 14.3 ounces with a standard deviation of .4 ounces. Jasmin purchases a box of the cookies. Having recently learned about means, standard
Brenda’s score was 90 on both her geology and math exams. The class mean for the geology exam was 87 with a standard deviation of 6. The class mean for the math exam was 82 with a standard
Harry’s score was 66 on an exam that had a mean of 57 and a standard deviation of 6.Find and interpret Harry’s z-score.
What are the mean and standard deviation for a z-distribution?
You scored at the mean on your first statistics test. What is your z-score?
Juanita took up running when she was 60 years old and has participated in a 5K race every year since. She is now 64. Her race times (in minutes) as well as the means and standard deviations for her
A set of scores follows: 6, 7, 8, 9, 10.a. Using the computational formula, calculate σ.b. Calculate s.c. Which is larger? Explain.
Use the computational formula to calculate SS, s2, and s for the following set of scores from a sample: 23, 42, 38, 29, 51, 37, and 44.
Use the definitional formula to calculate SS, σ2, and σ for the following set of scores from a population: 7, 10, 13, 9, and 6.
Calculate the range for the following scores: 2.5, 6.8, 3.4, 4.4, and 5.6. (Hint: you may need to revisit the topic of real limits from chapter 1.)
Calculate the range for the following scores: .48, .72, .81, .68, and .39. (Hint: you may need to revisit the topic of real limits from chapter 1.)
A set of scores follows: 36, 42, 28, 39, 27, 51, 32, 45, 59, 34, 71, 68.a. Determine the range.b. Determine the IQR.
What can you conclude?
The standard deviation of a distribution of scores was
Mathematically, how are the variance and standard deviation related?
Explain the difference between s and σ including the reason for the adjustment in s.
What is meant by the statement that “the sample standard deviation is a biased estimate of the population standard deviation”? What can be done about it?
What is a disadvantage and advantage of using definitional formulas?
Why is the range sometimes problematic as a measure of variability?
What is the preferred measure of variability for distributions that are skewed? Why?
The annual incomes for the employees of a new hat company are listed below (in thousandths). 65 33 52 47 72 73 68 65 58 49 18 59 31 62 61 74 42 27 54 52 80 78 66 22
Given the following set of scores: 8, 10, 10, 7, 12, 10, 8, 10, 7, 9a. what is the mode?b. what is the median?c. what is the mean?
Given the following set of scores: 6, 8, 3, 7, 9, 3, 7, 4, 7a. what is the mode?b. what is the median?c. what is the mean?
Decide which measure of central tendency should be used in the following situations:a. It is the only measure of central tendency that can be used for data measured on a nominal scale.b. It can only
What two factors need to be considered when deciding which measure of central tendency to report?
Why is it inappropriate to use the mean as a measure of central tendency in distributions that are skewed?
One of the presenters at an auto show wanted to know what color of motor vehicle is preferred. She asked the participants to choose from: black, white, blue, red, green, and tan. Which measure of
Dr. Hardnose is known for his difficult tests. The biology mid-term exam was no exception and many of the students obtained low scores. What measure of central tendency should be used to reflect the
Which measure of central tendency should be used when reporting the annual income of US households and why?
In a distribution of scores, the median was 60, the mean was 98, and the mode was 42.What is the shape of the distribution?
In a distribution of scores, the mode was 68, the median was 59, and the mean was 47.What shape is the distribution?
In a negatively skewed distribution, Tyron’s score was the same as the median, Jorge’s score was the same as the mode, and Geraldine’s score was the same as the mean.a. Who scored the
Discuss the locations of the mode, median, and mean in the normal distribution and in skewed distributions.
What is meant by the statement, “The sample mean is an unbiased estimate of the population mean?”
Define the three most common measures of central tendency and discuss their advantages and disadvantages.
Construct a grouped frequency distribution for the following set of scores:55 93 67 84 68 77 82 81 48 56 46 65 82 51 79 80 90 73 84 91
Given the following cumulative frequency distribution:X f cf 21 2 11 20 3 9 19 2 6 18 3 4 17 0 1 16 1 1a. What is N?b. What is the cumulative frequency of a score of 18?c. What is the percentile rank
For the following set of scores, first construct a simple frequency distribution. Then include columns for relative frequency, cumulative frequency, and percentile rank.25 30 23 27 28 22 27 28 26 29
The high score on a final exam in history was 84 and the low score was 22. Assume the professor constructs a grouped frequency distribution for the class.a. What is the range?b. What size of class
Discuss the characteristics of the normal distribution curve.
Discuss the differences between empirical and theoretical distributions.
Under what circumstances would you use a bar graph, histogram, and frequency polygon?
Identify the appropriate type of graph that should be used for the variables listed below:a. military rankb. intelligence scoresc. annual incomed. eye colore. letter gradesf. a comparison of life
Summation Operators:a. ΣX =b. ΣY=c. ΣX2 =d. ΣY2 =e. ΣXY =f. (ΣX)(ΣY) = g. (ΣX)2 = h. ΣX2 + ΣY2 = i. ΣX2 + (ΣY)2 = j. Σ(X – 1) = k. Σ(X – 1)2 = X Y x y2 XY (X-1) (X-1) 2440 3654 10
Using the correct order of operations, solve the following equations:a. (24 ÷ 8)2+ (13 + 4) + 52=b. [(23 – 17) – (69 ÷ 3)2+ 62] =c. [42+ (9 ÷ 3+32)] – 62=
Perform the calculations required for the following signed numbers:a. (–12) – (–8) =b. 10 + (–11) + 5 + (–5) =c. (6)(–2) =d. (–4)(–5) =e. (–28) ÷ (7) =f. (–80) ÷ (–20) =
There were 98 questions on Diego’s final psychology exam. He answered 85 of them correctly. Sofia answered 72 out of 80 questions correctly on her final geometry exam. Who scored higher?
In an English class of 35 students, 28 are female. In a history class of 60 students, 42 are male. Which class has a higher percent of females?
Write the following percentages as decimal proportions.a. 1%b. 28%c. 112%d. 364.7%
Round the numbers below to the nearest hundredth.a. 3.5151b. 64.5891c. 19.67843d. 36.998e. 3.86492
After drinking a beverage that contained 100, 200, or 300 mg of caffeine, research participants were asked to hold a pencil halfway inside of a tube while trying not to touch the tube with the
One group of students studied for their exam while listening to music. Another group studied in silence. Exam scores for the two groups were then compared. What are the independent and dependent
Research participants watched the same situational comedy either alone or with other participants. All participants then rated the funniness of the program. What are the independent and dependent
Identify the scale of measurement for the following variables:a. The number on football jerseysb. Scores on ability tests (IQ, GRE, SAT)c. Shirt size (small, medium, large)d. Reaction time
Determine the lower and upper limits for the values listed below.a. Hiking distance: 12.332 milesb. Words typed per minute: 48 wordsc. Time spent studying per week: 28.5 hoursd. Amount of water
Identify the following as either continuous or discrete variables.a. Number of desks in a classroomb. Distance from the earth to the moonc. Amount of time that your phone holds a charged. How many

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