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applied statistics and multivariate
Straightforward Statistics With Excel 2nd Edition Chieh-Chen Bowen - Solutions
Explain the law of large numbers in calculating probability
Identify the principal characteristics of the central limit theorem
Define sampling error, and explain why it is an unavoidable natural occurrence in empirical research
10. The ACT composite score is normally distributed, with a mean of 21.8 and a standard deviation of 5.4. What is the ACT composite score that separates the top 30% from the rest of the distribution?
9. A cardiologist studies heart rate variability. Heart rates are normally distributed, with a mean of 68 beats per minute and a standard deviation of 19 among a sample of 100 patients. What is the probability of randomly selecting a patient to obtain a heart rate less than 60?
7. The distribution of adult females’ BMI is normal, with µ = 27.1 and σ = 4.5. What proportion of the adult females have a BMI between 21 and 31?8. What is the probability of throwing two dice and getting the total number of dots as even numbers greater than six?
6. What is the answer for P(−2.05 < Z < −1.14)?1. .0202 2. .0668 3. .1069 4. .1271
5. Which of the following is true?1. P(Z > 2.0) > P(Z > 1.0)2. P(Z > −2.0) > P(Z > −1.0)3. P(Z > 0) > P(Z < 0)4. P(Z < −2.0) > P(Z < −1.0)
4. What is the probability that the total number of dots from throwing two dice is eight?1. 3/36 2. 4/36 3. 5/36 4. 6/36
3. What is the answer for P(−2.01 < Z < 1.45)?1. .0963 2. .9043 3. .8389 4. .1611
2. What is the answer for P(Z < 0.25)?1. .25 2. .75 3. .5987 4. −.4013
1. For a normal distribution, P(Z > 1.5) = .0668. What is P(Z < −1.5)?1. .0668 2. .9332 3. .9772 4. .0228
2. The probability of each value needs to be within 0 and 1, inclusive. It is expressed as 0 ≤ P(X) ≤ 1.
1. The variable X is a discrete, random, and numerical variable. The number of possible values of X is finite. Each value is associated with a probability.
3. SAT Evidence-Based Reading and Writing scores are normally distributed, with µ = 497 and σ = 115. SAT Math scores are normally distributed, with µ = 513 and σ = 117. A prestigious university only accepts students who score above the 90th percentile on SAT ERW and SAT Math. What SAT scores
2. Adult males’ body mass index (BMI) is normally distributed with µ= 26.1 and σ = 5.45. What proportion of adult males have a BMI between 21 and 39?
1. The total screen time spent on computers, smart devices, video games, and TV/movies tend to increase with age among children.However, higher screen time is associated with lower psychological well-being such as less curiosity, lower self-control, and worse emotional stability. The negative
2. If you cut the Z Table in the middle, the left side is a mirror image of the right side.3. P(Z > z) = 1 − P(Z < z).
1. All possible Z values under the normal distribution curve have a probability equal to 1.
6. Which one of the following attributes applies to the Z Table?
5. The connection between the probabilities and Z scores is made possible by 1. the multiplication rule of probability.2. the Addition Rule 1 of probability.3. the Addition Rule 2 of probability.4. the probability density function.
3. Which Z value sets the fastest 5% of swimmers’ times in a 100-meter freestyle race apart from the rest of the distribution?
2. What Z values set the boundaries of the middle 50% from the rest of the distribution?
1. What is the Z value that sets the top 1% apart from the rest of the distribution?
4. What is the probability of being within 0.5 standard deviations of the mean in the running speed?
3. What is the probability that your screen time is higher than 1.78 standard deviations above the mean for people your age?
2. What is the probability of being shorter than 0.25 standard deviations below the mean in height?
1. What is the probability that your workout time is less than 1.53 standard deviations above the mean?
4. If the problem statement asks for the probability of Z values larger than the specified z value, which is expressed as P(Z > z), it can be calculated as 1 minus the probability listed in the Z Table.
3. The intersection between the column and the row shows the area to the left of the specified z value or the probability of all Z values smaller than the specified z value, which is expressed as P(Z
2. The column represents Z values to one place after the decimal point, and the row represents Z values’ second place after the decimal point.
1. All Z values are reported to two places after the decimal point, and all probabilities are reported to four places after the decimal point.
4. What is the probability of throwing two dice to get the total number of dots greater than 4 and odd numbers?
4. The probability remains the same for every value.
3. The sum of the probabilities of all the values equals 1. It is expressed as ∑P(X) = 1
2. The probability of each value needs to be between 0 and 1, inclusive. This is expressed as 0 ≤ P(X) ≤ 1.
1. The variable X is a discrete, random, numerical variable. The number of possible values of X is finite. Each value is associated with a probability.
3. Which one of the following attributes is not required for constructing a probability distribution table?
4. The probability of a success is p = .5, and the probability of a failure is q = .5.
3. There are only two possible outcomes for each trial: success and failure.
2. The trials are independent of one another.
1. Which one of the following is not a required attribute of a binomial probability distribution?
4. The probability of a success and the probability of a failure remain the same in all trials.
3. There are only two possible outcomes for each trial: (1) success and (2) failure. These are commonly used labels. There is no value judgment involved. The outcomes can be head/tail or boy/girl.
2. The trials are independent events. The probabilities of outcomes in one trial do not affect the probabilities of outcomes in the other trials.
1. The procedure has a fixed number of trials.
Describe the purpose of using the Z Table?
Define Z score and explain the relationship between probability and Z score in a normal distribution
Identify and provide an example of a binomial probability distribution Explain how to construct a probability distribution table
Explain the addition rule, multiplication rule, and complementary rule in probability
Define probability terms such as simple event, event, and sample space
13. The national average of car insurance is $1,427 per year and standard deviation is $354. Alex paid $1,781 a year for his car insurance. What percentage of people paid more than Alex did on their car insurance?
12. According to the College Board, the SAT ERW µ = 497 and σ= 115, and the Math µ = 513 and σ = 120. Ted’s ERW score was 730, and his Math score was 760. Were Ted’s scores considered unusual scores?
11. Robin scored 40 points on an English test with and s =8. He also scored a 50 on a math test with and s =5. In which subject did Robin perform better than his classmates?
10. Which one of the following distributions with X = 60 has the smallest Z score?1. µ = 50 and σ = 60 2. µ = 50 and σ = 30 3. µ = 50 and σ = 15 4. µ = 50 and σ = 10
9. Which one of the following distributions where X = 70 would have the highest Z value?1. µ = 100 and σ = 60 2. µ = 100 and σ = 30 3. µ = 100 and σ = 15 4. µ = 100 and σ = 10
8. In a sample n = 5, all the raw scores are converted into Z scores.The first four Z scores are −1.19, −0.69, 0.75, and 1.12. What is the last Z score?
7. In an IQ test with mean = 100 and standard deviation = 15, what score is 1.5 standard deviations above the mean (Z = 1.50)?1. 100 2. 115 3. 122.5 4. 130
6. A sample of n = 78 scores are transformed into Z scores. The standard deviation for the 78 Z scores __________ 1. is 0 2. is 1 3. is −1 4. cannot be determined without more information.
5. For a sample with a score of X = 40 corresponds to Z = 0.50. What is the standard deviation for the sample?1. 2 2. 4 3. 8 4. 16
4. Under a normal distribution curve, the area covered by µ ± 2σ is roughly __________% of the data.1. 50 2. 68 3. 95 4. 99
3. A sample of n = 45 scores are transformed into Z scores. The mean for the 45 Z scores __________.1. is 0 2. is 1 3. is −1 4. cannot be determined without more information
2. A sample of n = 63 scores has a mean of and a standard deviation of s = 8. In this sample, what is the Z score corresponding to X = 39?1. Z = 0.75 2. Z = 1.00 3. Z = −0.75 4. Z = −1.00
1. For a population with µ = 100 and σ = 20, what is the X value corresponding to Z = 0.50?1. 90 2. 95 3. 105 4. 110
2. If all the reaction times were converted to Z scores, what was the shape of the Z-score distribution?
1. What was the standard deviation of reaction time in this sample?
8. What percentage of students scored higher than Bianca?1. 16%2. 32%3. 68%4. 84%
4. Assume that the scores on a statistics exam were normally distributed. Bianca earned 74 points on the exam. The exam scores had?
3. Based on the empirical rule, 99.7% of values are within 3 standard deviations from the mean, −3 ≤ Z ≤ 3. What percentage of values fall within 0 ≤ Z ≤ 3?
2. What is the measurement unit of Z scores?1. The same as the measurement unit of the original scores 2. The square of the measurement unit of the original scores 3. The square root of the measurement unit of the original scores?
1. For a population with µ = 100 and σ = 10, what is the X value corresponding to Z = 0.75?1. 92.5 2. 97.5 3. 105 4. 107.5
3. How short would a woman have to be to have Z = −1.25?
2. How tall would a woman have to be to reach Z = 2?
1. What is the Z score for a woman with a height of 5 feet 3 inches?
Apply the empirical rule to connect Z scores with probabilities in special cases?
Calculate Z scores for population or sample data Explain how converting raw scores to Z scores does not change the shape of the distribution
Identify unusual values or outliers using Z scores
Convert raw scores to Z scores to get measures on a universal yard stick
15. In a randomly selected sample of 21 students who took statistics courses this semester, their midterm exam grades are reported in Table 3.12. Use Excel to calculate the measures of variability for these 21 students’ exam grades.
14. If you think the drive-through service at fast-food restaurants is slow, you are not alone. A market research firm studied and reported fast-food drive-through time. Here is a sample of 55 randomly selected customers and their drive-through time as shown in Table 3.11. What are the measures of
13. In a randomly selected sample of 50 women, shoe sizes are measured and reported in Table 3.10. What are the measures of variability for these 50 women’s shoe sizes?
12. Which one of the following measures of variability only involved extreme values of the sample?1. Range 2. Variance 3. Standard deviation 4. Sum of squares
11. The round-off rule states that the final values for measures of variation should be reported 1. with the same decimal places as in the original data 2. with one more decimal place than in the original data 3. with two more decimal places than in the original data 4. with three more decimal
10. Which of the following statements is correct?1. The degrees of freedom for sample variance are n − 1 2. The degrees of freedom for population variance are n − 1 3. The degrees of freedom for sample standard deviation are n 4. SS means sum of standard deviations
9. What is the SS for the following sample data: 10, 7, 6, 10, 6, and 15?1. 60 2. 36 3. 100 4. −25
8. The relationship between variance and standard deviation is that 1. standard deviation is smaller than variance 2. standard deviation is larger than variance 3. standard deviation is the square root of the variance 4. standard deviation is equal to variance
7. For the scores 3, 3, 5, 7, 14, and 16, what is the correct answer for 1. −6 2. 0 3. +6 4. 160
6. In a sample of 45 homework grades, the highest score is 10 and the lowest score is 5. The range for homework grades is __________.1. 5 2. 6 3. 22.5 4. 23
5. Variance is one of the measures for variability that requires the variable to be __________ scales of measurement.1. nominal, ordinal, interval, and ratio 2. ordinal, interval, and ratio
4. When there are 12 observations in a small sample, the degrees of freedom for the sample standard deviation is __________.1. 10 2. 11 3. 12 4. 13
3. In a population of 20 members, the sum of squares (SS) of variable X is 314, what is the standard deviation of variable X?1. 4.06 2. 3.96 3. 3.76 4. 3.54
2. In a sample where the sum of squares (SS) of variable X is 112 and the sample size is 25, what is the variance of variable X?1. 4.96 2. 4.67 3. 4.48 4. 4.12
1. In a sample where the variance of variable X is 24, what is the standard deviation of X?1. 23 2. 18.57 3. 5.0 4. 4.90
2. Variance and standard deviation are more reliable and more frequently used than range. Be careful in choosing the correct formula when calculating variance and standard deviation in a population versus in a sample.
1. Range is the maximum minus the minimum in the distribution, which is highly sensitive to extreme values.
2. Use Excel to calculate the variance and standard deviation of these 20 students’ study hours.
1. Use adjusted statistical formulas when using a frequency table to answer this question.
Apply the correct formulas to calculate variance and standard deviation in populations or samples?
Calculate variance and standard deviation using Excel
Adjust formulas to calculate variance and standard deviations when using frequency tables
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