Statistics In Plain English 4th Edition Timothy C. Urdan - Solutions

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Use permutation and combinations to count the number of outcomes in both an event and the sample space
Interpret probabilities and use probabilities of outcomes to calculate probabilities of events in discrete sample spaces
Understand and describe sample spaces and events for random experiments with graphs, tables, lists, or tree diagrams
Discuss how probability and probability models are used in engineering and science
Explain the differences between mechanistic models and empirical models
Identify the advantages that designed experiments have in comparison to other methods of collecting engineering data
Discuss the different methods that engineers use to collect data
Explain the difference between enumerative and analytical studies
Discuss how variability affects the data collected and used for making engineering decisions
Identify the role that statistics can play in the engineering problem-solving process
7. From a conceptual standpoint, how is the Environmental survey item with the weakest contribution to the Cronbach’s alpha different from the other three Environmental items? And how is this difference reflected in the cross-loading of this item on two factors?
6. What does the information provided in Table 15.10 suggest regarding which item, if any, might be eliminated from the Environmental items to create a good scale?
5. Looking at the factor loadings from the Rotated Factor Matrix in Table 15.9, what would you predict the Cronbach’s alpha to be for the four Social items? Why?
4. Using the information from the Rotated Factor Matrix in Table 15.9, which items are cross-loading on more than one factor? What does this tell you about these items?
3. Using the information about eigenvalues and percentage of variance explained in Table 15.9, how many solid factors do you think emerged from the factor analysis of the survey items?Why do you think so?
2. What does a reliability analysis tell you?
1. What is the purpose of conducting a factor analysis?
8. Suppose that in a large company, there is an allegation of gender bias in relation to who receives promotions and who does not. Explain how the chi-square test of independence compares observed and expected frequencies to determine whether this allegation is true.
7. Explain when you would use a nonparametric test rather than a parametric test.
6. What does the chi-square statistic that you calculated tell you? What doesn’t it tell you?
5. Compare the critical value from Appendix E with the observed chi-square value that you calculated in Question 2 and decide whether your observed value is statistically significant.
4. Using the df you just calculated, and an alpha level of .05, find the critical value for the chi-square statistic in Appendix E.
3. Report the degrees of freedom (df) for this problem.
2. Calculate the sum of squared differences between the observed and expected values to find the observed chi-square value.
1. Calculate the expected values for each of the six cells in the table.
7. Now suppose that I add a second predictor variable to the regression model: hours per week spent working for money. And suppose that the correlation between hours spent working and hours spent studying is −.50. The correlation between the two predictor variables (number of close friends and
6. Regression is essentially a matter of drawing a straight line through a set of data, and the line has a slope and an intercept. In regression, how is it decided where the line should be drawn?In other words, explain the concept of least squares.
5. What, exactly, is a residual (when talking about regression)?
4. If you know that somebody studied had 10 close friends, how many hours per week would you expect them to study?
3. Calculate the intercept and wrap words around your result.
2. What would the value of the standardized regression coefficient be in this problem? How do you know?
1. Assume that “hours spent studying” is the Y variable and “close friends” is the X variable.Calculate the regression coefficient (i.e., the slope) and wrap words around your results.What, exactly, does this regression coefficient tell you?
7. Calculate a 95 percent confidence interval for this correlation coefficient and interpret it.What does it tell you?
6. Calculate the observed t value and decide whether this correlation coefficient is statistically significant using an alpha level of .05. Interpret your results. What do they tell you?
5. Using Appendix B and an alpha level of .05, find the critical t value.
4. Calculate the coefficient of determination and interpret it. What does it tell you?
3. Interpret this correlation coefficient. What does it tell you?
2. What is the strength of this correlation coefficient? How do you know?
1. What is the direction of this correlation coefficient? How do you know?
6. Using the information from the graphs that you created and the statistics about the main effects and the interaction effects, write a summary statement about what you now know about how students’ perceptions of their teachers’ emphasis on Mastery (i.e., learning and understanding) changed
5. Create two graphs of the means: first a column graph and then a line graph. Be sure to include all four time points for each of the grade levels.
4. Is the interaction between Mastery Emphasis and grade level statistically significant? What does this interaction tell you?
3. What is the effect size for the within-subjects effect for Mastery Emphasis?
2. The main effect for grade level is not statistically significant. What does that mean, exactly?
1. How many of the participants in this study were in ninth grade and how many were in eleventh grade in the first year of the study?
7. How much of the variance in GPA is explained by gender, generation, and their interaction combined?
6. Combining the information for the three main tests of effects (i.e., main effects for gender and generation, interaction effect for gender × generation), write a sentence that summarizes these tests of statistical significance.
5. Using the degrees of freedom for generation and for error and the values in Appendix C, what is the critical value for F if the alpha level is .05?
4. Is there a statistically significant interaction between gender and generation on GPA?
3. Based on the summary statistics in Table 10.6, what is the effect size for the main effect of generation? What does this effect size tell you?
2. Based on the summary statistics in Table 10.6, is the difference between the GPAs of boys and girls statistically significant?
1. Just looking at the means presented in Table 10.5, predict whether there will be statistically significant main effects for gender and generation and a significant interaction between the two.
5. Suppose I want to know whether drivers in Ohio, Texas, and California differ in the average number of miles they commute to work each day. So I select random samples of 5 drivers from each state and ask them how far they drive to work. I get the data that is summarized in Table 9.10. Please
4. How should we interpret a significant F ratio? That is, what does a statistically significant F ratio tell us? What does it not tell us?
3. Describe what an F ratio is. What does it tell you?
2. Why would we use ANOVA rather than multiple t tests?
1. What type of research question would you use ANOVA to answer?
3. I think people are getting taller. I select a random sample of 15 fathers and their adult sons to take part in a study. I find that the fathers have an average height of 71 in. and their sons have an average height of 73 in. The standard deviation of the difference between the means is 1.3.a.
2. Suppose you want to know whether men and women who take a college statistics class differ in their enjoyment of statistics. Enjoyment of statistics is measured by asking people to rate“How much do you enjoy statistics?” on a 10-point scale (1 = “I hate it” and 10 = “I love it”).I
1. I want to know whether Californians, who tend to be pretty health conscious, eat fewer hot dogs than the general population of Americans. Suppose that in the population of adults, the average number of hot dogs eaten per year is 15. I select a random sample of 25 adults from California and find
8. How does sample size affect whether a result is statistically significant?
7. If we know that a result is statistically significant, why should we calculate an effect size and a confidence interval? What additional information is gained from these statistics?a. Please discuss the difference between practical significance and statistical significance in this answer.
6. What does it mean to say that a result is statistically significant?
5. What, exactly, does a p value tell you?
4. Calculate two confidence intervals and explain what they indicate.a. First, calculate a 95 percent confidence interval for the sample mean.b. Then calculate a 99 percent confidence interval for the difference between the sample mean and the population mean, assuming the population mean is
3. Calculate a Cohen’s d statistic and interpret it. Would this be considered a small, moderate, or medium effect size?
2. Is the difference between the sample mean and the population mean statistically significant?
1. Write the null and alternative hypotheses for this problem, once using symbols and again in sentence form.
8. Explain how you would decide whether to calculate a z score or a t value to determine the probability of randomly selecting a sample with a given mean by chance from a population?
7. Explain why it makes sense that the larger sample size produces the difference in the two probabilities that you obtained in Questions 2 and 5.
6. Using this larger sample size of 36, and the standard deviation from the population, calculate a new probability of obtaining a difference between the sample mean and the population mean that is this large by chance.a. Compare this probability with the probability that you obtained in Question
5. Suppose that instead of a sample size of 16, you had a sample size of 36.a. How would this affect the size of the standard error of the mean?b. Why does it make sense that a larger sample size has this effect on the size of the standard error of the mean?
4. Compare the two standard errors that you calculated in Questions 2 and 3. Why are they different?
3. Using the standard error of the mean that you calculated using the sample standard deviation, develop an estimate of the probability of getting a difference between the sample mean and the population mean that is this large by chance. (Note: This is a t value problem.)a. Describe your results.
2. Using the standard error of the mean that you calculated using the population standard deviation, determine the probability of getting a difference between the sample mean and the population mean that is this large by chance. (Note: This is a z score problem.)a. Describe your results. What does
1. Calculate two standard errors of the mean, one using the population standard deviation and the other using the sample standard deviation. Describe what each of these standard errors tells you.
6. What is the probability of randomly selecting an individual from the population who takes 8 vacation days or more off?
5. Suppose that you randomly select an individual from the population who takes 20 vacation days off per year. Calculate that person’s z score and interpret it. What does it tell you?
4. What percentage of the distribution takes between 6 and 15 vacation days off per year?
3. What proportion of the distribution takes between 6 and 10 vacation days off per year?
2. What is the number of vacation days that marks the 30th percentile of this distribution?
1. What percentage of the population takes at least 7 vacation days off per year?
5. If you know that in the population of adults, the average number of hours slept per night is 7, with a standard deviation of 2, what proportion of the population would you expect to sleep between 7 and 9 hours per night?
4. Many believe that most human traits form a normal distribution. Height, weight, intelligence, musical ability, friendliness, attractiveness, etc. are all examples of things that might form a normal distribution.a. First, explain whether you agree with this assumption, and why or why not.b.
3. In statistics, we use the normal distribution a lot.a. What is so great about it? In other words, what does it do for us?b. Describe something that the normal distribution lets us, as statisticians, do that we cannot do without it.
2. What does “asymptotic” mean and why is it important?
1. In statistics, the word “distribution” comes up a lot.a. In your own words, explain what a distribution is.b. Then, again in your own words, explain what a “normal distribution” is.
7. Think of an example that illustrates why it is important to know about the standard deviation of a distribution.
6. Explain why the standard deviation you reported for Question 3 differs from the standard deviation you reported for Question 5.
5. Pretend that this distribution of scores represents a population rather than a sample. Calculate and report the standard deviation and explain what it tells you.
4. Write a sentence or two in which you explain, using your own words, what a standard deviation is (in general, not this particular standard deviation).
3. Calculate and report the standard deviation of this distribution.
2. Calculate and report the variance of this distribution.
1. Calculate and report the range of this distribution.
5. If you have calculated the mean and the median correctly, you will notice that the median is larger than the mean. What caused this difference between the mean and the median?Explain your answer.
4. Do you believe this distribution is skewed in one direction or another? Why do you think so?
3. What is the mean of this distribution?
2. What is the median of this distribution?
1. What is the mode of this distribution?
9. How could you re-design this study to get results from the sample data that would be more generalizable to the population(s)?

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Statistics In Plain English 4th Edition Timothy C. Urdan - Solutions

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