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statistics informed decisions using data

Questions and Answers of Statistics Informed Decisions Using Data

Comment on using the Wilcoxon-Mann-Whitney test when the goal is to compare medians.
When the Wilcoxon-Mann-Whitney rejects, how should this be interpreted?
You want to compare the effects of two different cold medicines on reaction time.Suppose you measure the decrease in reaction times for one group of participants who take one capsule of drug A, and
For the data in the previous exercise, apply the Kolmogorov-Smirnov test, again using α = .05. (It is interesting to note that if an exact critical value is used, rather than the approximate
When there are many tied values, speculate on whether the Wilcoxon-Mann-Whitney test will have more power than the Kolmogorov-Smirnov test.
Two methods for reducing shoulder pain after laparoscopic surgery were compared by Jorgensen et al. (1995). The data were Group 1: 1,2,1,1,1,1,1,1,1,1,2,4,1,1 Group 2: 3,3,4,3,1,2,3,1,1,5,4.Compare
Imagine two groups of cancer patients are compared, the first group having a rapidly progressing form of the disease and the other having a slowly progressing form. At issue is whether psychological
Repeat the previous problem, only use the Kolmogorov-Smirnov test.
For three independent groups, you observe Group 1: 4,6,7,8,9,15,12,19 Group 2: 16,18,2,21,29,30,24,27 Group 3: 20,22,26,31,32,38,39,41.Perform the Kruskal-Wallis test with α = .05.
In the previous exercise, the largest observation is 41, which is in the third group.The sample means can be seen to be 10, 20.9, and 31.1, respectively, and the ANOVA F test in chapter 10 rejects
For two dependent groups you get Group 1: 10, 14, 15, 18, 20, 29, 30, 40 Group 2: 40, 8, 15, 20, 10, 8, 2, 3.Compare the two groups with the sign test and the Wilcoxon signed rank test with α = .05.
For two dependent groups you get Group 1: 86 71 77 68 91 72 77 91 70 71 88 87 Group 2: 88 77 76 64 96 72 65 90 65 80 81 72.Apply the Wilcoxon signed rank test with α = .05
Show by numerical example that X2 i is not necessarily equal to (Xi) 2.
Find the mean and median of the following sets of numbers. (a) −1, 03, 0, 2, −5.(b) 2, 2, 3, 10, 100, 1,000.
The final exam scores for 15 students are 73, 74, 92, 98, 100, 72, 74, 85, 76, 94, 89, 73, 76, 99.Compute the mean and median.
The average of 23 numbers is 14.7. What is the sum of these numbers?
Consider the ten values 3, 6, 8, 12, 23, 26, 37, 42, 49, 63.The mean is X¯ = 26.9.(a) What is the value of the mean if the largest value, 63, is increased to 100?(b) What is the mean if 63 is
Repeat the previous problem, only compute the median instead.
In general, how many values must be altered to make the sample mean arbitrarily large?
In general, approximately how many values must be altered to make the sample median arbitrarily large?
For the values 0, 23, −1, 12, −10, −7, 1, −19, −6, 12, 1, −3, compute the lower and upper quartiles (the ideal fourths).
For the values −1, −10, 2, 2, −7, −2, 3, 3, −6, 12, −1, −12, −6, 8, 6, compute the lower and upper quartiles (the ideal fourths).
Approximately how many values must be altered to make q2 arbitrarily large?
Argue that the smallest observed value, X(1), as well as the the lower and upper quartiles, satisfy the definition of a measure of location.
The height of 10 plants is measured in inches and found to be 12, 6, 15, 3, 12, 6, 21, 15, 18 and 12.Verify that (Xi −X¯) = 0.
For the data in the previous problem, compute the range, variance and standard deviation.
Use the rules of summation notation to show that it is always the case that(Xi −X¯) = 0.
Seven different thermometers were used to measure the temperature of a substance. The readings in degrees Celsius are −4.10, −4.13, −5.09, −4.08,−4.10, −4.09 and −4.12. Find the
A weightlifter’s maximum bench press (in pounds) in each of six successive weeks was 280, 295, 275, 305, 300, 290.Find the standard deviation.
For the values 20,121,132,123,145,151,119,133,134,130, use the classic outlier detection rule to determine whether any outliers exist.
Apply the boxplot rule for outliers to the values in the preceding problem.
Consider the values 0,121,132,123,145,151,119,133,134,130,250.Are the values 0 and 250 declared outliers using the classic outlier detection rule?
Verify that for the data in the previous problem, the boxplot rule declares the values 0 and 250 outliers.
Consider the values 20,121,132,123,145,151,119,133,134,240,250.Verify that no outliers are found using the classic outlier detection rule.
Verify that for the data in the previous problem, the boxplot rule declares the values 20, 240, and 250 outliers.
What do the last three problems suggest about the boxplot rule versus the classic rule for detecting outliers?
What is the typical pulse rate (beats per minute) among adults? Imagine that you sample 21 adults, measure their pulse rate and get 80,85,81,75,77,79,74,86,79,55
For the observations 21,36,42,24,25,36,35,49,32 verify that the sample mean, trimmed mean and median are X¯ = 33.33, X¯t = 32.9 and M = 35.
The largest observation in the last problem is 49.If 49 is replaced by the value 200, verify that the sample mean is now X¯ = 50.1 but the trimmed mean and median are not changed.
For the last problem, what is the minimum number of observations that must be altered so that the trimmed mean is greater than 1,000?
Repeat the previous problem but use the median instead. What does this illustrate about the resistance of the mean, median and trimmed mean?
For the observations 6,3,2,7,6,5,8,9,8,11 verify that the sample mean, trimmed mean and median are X¯ = 6.5, X¯t = 6.7 and M = 6.5.
In general, when you have n observations, what proportion of the values must be altered to make the 20% trimmed mean as large as you want.
A class of fourth graders was asked to bring a pumpkin to school. Each of the 29 students counted the number of seeds in their pumpkin and the results were
Compute the 20% Winsorized values for the observations 21,36,42,24,25,36,35,49,32.
For the observations in the previous problem, compute the sample 20%Winsorized variance.
In the previous problem, would you expect the sample variance to be larger or smaller than 51.4? Verify your answer.
In general, will the Winsorized sample variance, s 2w, be less than the sample variance, s 2?
For the observations 6,3,2,7,6,5,8,9,8,11 verify that the sample variance and Winsorized variance are 7.4 and 1.8, respectively.
Consider again the number of seeds in 29 pumpkins given in problem 34.Compute the 20% Winsorized variance.
Snedecor and Cochran (1967) report results from an experiment dealing with weight gain in rats as a function of source and amount of protein. One of the groups was fed beef with a low amount of
A family doctor is interested in examining the relationship between a patient's age and total cholesterol (in \(\mathrm{mg} / \mathrm{dL}\) ). He randomly selects 14 of his female patients and
Compute the standard error of the estimate for the data in Table 1.Approach Use the following steps to compute the standard error of the estimate.Step 1 Find the least-squares regression line.Step 2
Test whether a linear relation exists between age and total cholesterol at the \(\alpha=0.05\) level of significance using the data in Table 1 from Example 1.Approach Verify that the requirements to
Determine a 95% confidence interval for the slope of the true regression line for the data presented in Table 1 in Example 1.By-Hand ApproachStep 1 Determine the least-squares regression line.Step 2
Use the data in Table 4.(a) Find the least-squares regression equation \(\hat{y}=b_{0}+b_{1} x_{1}+b_{2} x_{2}\), where \(x_{1}\) represents the patient's age, \(x_{2}\) represents the patient's
For the model obtained in Example 2, determine the coefficient of determination and the adjusted \(R^{2}\). Compare the \(R^{2}\) with the two explanatory variables age and daily saturated fat to the
Construct a 95% confidence interval for a mean response and a 95% prediction interval for an individual response for a 32-year-old female who consumes 23 grams of saturated fat daily using the model
Using the data presented in Table 5:(a) Find the correlation matrix among all three variables.(b) Find the least-squares regression model using both \(x_{1}\) and \(x_{2}\) as explanatory
The wind chill index represents what the air feels like on exposed skin while factoring in wind speed. The wind chill index is determined by considering the wind speed at a height of 5 feet, the
The data in Table 7 represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender.(a) Draw a scatter diagram of the data treating
Researchers developed a model to predict the age, \(y\), of an individual based on the gender of the individual, \(x_{1}(0=\) female, \(1=\) male \()\), the height of the second premolar, \(x_{2}\),
Photosynthetic efficiency is the percentage of light energy that is converted into chemical energy by a plant. The chemical energy is used by a plant to maintain the plant's activities. A sample of
The data in Table 9 represent the miles per gallon (MPG) along with potential explanatory variables weight (in thousands of pounds), number of cylinders, and horsepower. Use a partial \(F\)-test to
An engineer wants to develop a model to describe the gas mileage of a sport utility vehicle. He collects the data presented in Table 10. The final drive ratio is the ratio of the gear set that is
Use the backward elimination procedure to find the best model to describe miles per gallon for the data in Table 10. Use a level of significance of \(\alpha=0.05\) as the criteria for an explanatory
Crickets make a chirping noise by sliding their wings rapidly over each other. Perhaps you have noticed that the number of chirps seems to increase with the temperature. The following table lists the
We record the gender of the 15 students enrolled in an introductory statistics course as they enter the classroom. The males are denoted by a blue M and the females are denoted by a red
Prosthodontists specialize in the restoration of oral function, including the use of dental implants, veneers, dentures, and crowns. Since repairing chipped veneer is less costly and time-consuming
The researcher in Example 1 wants to determine if there is a difference in the mean shear bond strength among the four treatment groups at the \(\alpha=0.05\) level of significance.Approach We will
In Example 3 from Section 13.1, we rejected the null hypothesis \(H_{0}: \mu_{\text {Cojet }}=\mu_{\text {Silistor }}=\mu_{\text {Cimara }}=\mu_{\text {Ceramic }}\). Use Tukey's test to determine
Zocor is a drug manufactured by Merck and Co. that is meant to reduce the level of LDL (bad) cholesterol and increase the level of HDL (good) cholesterol. In clinical trials of the drug, patients
Invest in Education Go to the book's website to obtain the data file 14_1_17. The variable "2013 Cost" represents the fouryear cost including tuition, supplies, room and board, the variable "Annual
Interpret the regression coefficients for the least-squares regression equation found in Example 2.Approach Interpret the coefficients the same way as we did for a regression with one explanatory
What was the mean price of the security on the first of January 2004?
How would you describe the price movement of the security during the third quarter (01-July-2004 to 01-Oct-2004)?
What is the change in value for this security over the four quarters recorded in the high–low–close graph?
Which of the three quarters exhibited the most consistent increase in value for this security?
For the year 1995, what are the maximum sales for women’s clothing and the minimum for men’s?
What are the medians for the range (maximum to minimum) for the years 1989 and 1998? Was there an identifiable trend over the 10 years between these two values?
What happened to the average sales figures for jewelry over the 10-year period?
Which of the 10 years had the most and least variability between the maximum sales of women’s clothing and the minimum for men’s, and what were those ranges?
Which of the two groups, those that defaulted or did not, had the most variability for the maximum in other debt and the minimum for their credit card debt?
What are the ranges (maximum other debt and the minimum credit card debt) for those defaulting and those that have not, and which is the smallest?
Can you identify a pattern between the two groups representing those that have defaulted and those that have not for the debt-to-income and the size of their ranges?
Which groups have the largest and smallest mean debt-to-income ratio?
What are the mean differences for all educational groupings on default history?
In which of the five educational categories does the default history have the least impact on the debt-to-income ratio?
Which of the 10 groups has the most and the least variability in the maximum other debt and minimum credit card debt?
(a) In which month was the highest sale of women’s clothing recorded and what was that amount?(b) What direction did the mean of the range bar move between months 11 and 12?(c) What direction did
(a) What is the age of the oldest male who has a college degree?(b) What is the fewest number of years of education for the females?(c) Which category for both males and females has the most years of
(a) What is the age of the oldest person who has earned a college degree?(b) What is the fewest number of years of education attained by any of the respondents?(c) Which category has the most years
(a) What is the lowest price of the stock, and approximately when did this occur?(b) What is the highest price of the stock, and approximately when did this occur?(c) Which month for purchasing the
(a) Is there a significant difference in the ages for the married and unmarried groups?(b) What is the minimum income for unmarried individuals before the work program?(c) What is the maximum income
(a) What percentage of White respondents have no children?(b) What percentage of Black respondents have five children?(c) What percentage of respondents who belong to the Other Category have four
(a) What percentage of those who live in the North East have an exciting life?(b) What percentage of those who live in the South East have a Routine life? (c)What percentage of those who live in the
(a) What is the most years of education obtained by minorities and nonminorities?(b) What is the trend in earnings for the nonminority after 15 years of education?(c) What is the highest salary
(a) What is the oldest age interval for those who did not complete high school, and how many are in that interval?(b) Which age interval and level of education classification contains the largest
(a) What percentage of the total respondents are White and have no children?(b) What percentage are Black and have no children?(c) What percentage belongs to the Other category and have no
What job category, for males, has the highest percentage of employees?

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