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essentials of statistics
Questions and Answers of
Essentials Of Statistics
Using the test the research hypothesis at the .05 level of significance that males raise their hands in class more often than females. Do this practice problem by hand using a calculator. What is
Using the data in the file, test the null hypothesis that urban and rural residents have the same attitudes toward gun control. Use the T.TEST function to test the hypothesis. Assume that the
For your Friday afternoon report to the boss, you need to let her know if the two stores in Newark, New Jersey (your author's fair city of origin), are selling the same amount of merchandise each
During the last football season, the Brutes managed to gain an average of 203 yards per game while their opponents averaged 288 yards per game. Fire the coach?
What would it mean if a difference were statistically significant but the effect size were not meaningful?
What is the difference between a test of independent means and a test of dependent means, and when is each appropriate?
Compute the \(t\) value using the Data Analysis tools and write a conclusion as to whether there was a change in tons of paper used as a function of the recycling program in 25 districts. Test the
In the following examples, indicate whether you would perform a \(t\)-test of independent means or dependent means.a. Two groups were exposed to different levels of treatment for ankle sprains. Which
Compute the \(t\) value (do it manually, argh!) and write a conclusion as to whether there was a change in a group of families' satisfaction level (the higher the score, the more satisfied) with
Here's a tough one. For the same data where two groups are being compared, the critical value for rejection of the null hypothesis is higher for a set of dependent groups than for a set of
Ace used-car sales manager Jack has no idea whether the \(\$ 100,000\) he pays for training for his used-car salespeople works. He asks Dave, the leading salesperson, and Dave says he thinks it works
Whether counseling adolescents at the beginning of the school year had a positive impact on their tolerance for other adolescents who are ethnically different from them. Assessments were made right
A comparison is shown between yards rushing for the first and last games of the season for 10 different football teams. Which team is best? And, yes, this is a trick question-can you find the trick?
Using the following table, provide three examples of a simple one way ANOVA, two examples of a two-factor ANOVA, and one example of a three-factor ANOVA. We show you some examples. Be sure to
Compute the \(F\) value for a comparison among the three levels representing the average amount of time that swimmers practice weekly ( \(25\) hours), with the dependent or outcome variable being
Stephen recognizes that there are different techniques for attracting attention to advertisements, and he wants to test three of these for the sample product: all color, all black-and-white, and a
The researchers want to find out whether there is a difference among the graduation rates (and these are percentages) of five high schools over a 10 -year period. Is there? (Hint: Are the years a
Contains the average sales for five stores across four seasons. Which season was the best of all for sales?
When would you use a factorial ANOVA rather than a simple ANOVA to test the significance of the difference between the averages of two or more groups?
Create a 23 experimental design that would lend itself to a factorial ANOVA.
Complete the analysis and interpret the results. It is a 2 3 experiment: There are two levels of severity, where Level 1 is severe and Level 2 is mild, and there are three levels of treatment,
Show the results of an experiment in which three levels of nutrition education and two levels of dietary intervention were tested to see their effects on a 10 -point scale, with 10 indicating the
You can find a 3 4 design with three levels of participation in after-school activities and four levels of GPA (1st, 2nd, 3rd, or 4th quartile). The outcome is success (as measured by peer rating)
Given the following information, use -Table B. 4 in Appenclix B to determine whether the correlations are significant and how you would interpret the results.a. The correlation between speed and
Discuss the general idea that just because two things are correlated, one does not necessarily cause the other. Provide an example (other than ice cream and crime!).
Betsy is interested in predicting how many 75 -year-olds will develop Alzheimer's disease and is using as predictors level of education and general physical health graded on a scale from 1 to 10 .
You're interested in predicting success in business. You're a stats star! Why not go out and collect 15 different variables and combine them to see which combination best predicts success (however
Go to the library and locate three examples of research studies in your area of interest in which linear regression was used. It's okay if a study contains more than one predictor variable. Answer
Here's where you can apply the information in one of this chapter's tips and get a chance to predict a Super Bowl winner! Coach Kent is curious to know whether the average number of games won in a
Why is the standard error of estimate or prediction higher when the predictive quality of variables is lower?
You will find scores on three variables. The outcome variable is overall health (Health)-the higher the score, the healthier the person is. The predictor variables are preference for sweets (Sweets),
Reach a conclusion as to whether number of years of training makes a good chef (and the higher the better on the Chef's Score).
Using the following data, test the question of whether an equal number of Democrats, Republicans, and independents voted during the most recent election. Test the hypothesis at the .05 level of
Using the following data, test the question of whether an equal number of boys and girls participate in soccer at the elementary level at the .01 level of significance. What's your conclusion? Gender
Of the following four research questions, which ones are appropriate for the chi-square test?a. What is the difference between the average scores of two math classes?b. What is the difference between
At the Diabetes Institute, patients are classified as compliant (they take their medication as they should) or not (they don't). A new program manager has a new idea: Have some patients continuously
Create formulas for the following in an Excel worksheet:a. Add the values of 3 and 5 to one another.b. Subtract the value of 5 from 1 O and multiply the outcome by 7.c. Average the values 5, 6, 7,
Use the AVERAGE function to add the values of 3, 5, and 7 and divide the total by 3.
What would the function look like for summing the values in Cells A 1 through AS?
What would the function look like for averaging the values in Cells A 1 through AS?
Create a worksheet with any five values in Cells A 1 through AS, name the range of these cells Test_Scores, and enter a function in Cell A6 that computes the average. Can you think of another way to
Compute the mean, median, and mode for the following three sets of scores. Do it by hand or using Excel. Show your work, and if you are using Excel, print out a copy of the output. Score 1 Score 2
Find out the average number of times children in three different classes ask a question each day of the week. What measure of central tendency did you use and why?
You are the manager of a fast-food store. Part of your job is to report to the boss at the end of each day which special is selling best. Use your vast knowledge of descriptive statistics to write
Under what conditions would you use the median rather than the mean as a measure of central tendency? Why? Provide an example of two situations in which the median might be more useful than the mean
List three variables, and how they are measured, for which you would use the mode as the most appropriate measure of central tendency.
You're in business for yourself and you have been fortunate to buy and own the website titled Havefun.com, where you sell every imaginable stupid toy (like potato guns) and games that everyone needs.
Compute the median sales for all three toys.
Suppose you are working with a data set that has some very "different" (much larger or much smaller than the rest of the data) scores. What measure of central tendency would you use and why?
As the head of public health, you conduct a weekly census across age-groups of the number of cases of flu reported in your area. By hand, compute the mean and the median by week. Which do you think,
Why is the range the most convenient measure of dispersion yet the most imprecise measure of variability? When would you use the range?
Compute the exclusive and inclusive ranges for the following items. High Score Low Score Inclusive Range Exclusive Range 7 6 89 45 34 17 15 2 1 1
For the following set of scores, compute the range, the unbiased and the biased standard deviation, and the variance. Do these computations by hand. 31, 42, 35, 55, 54, 34, 25, 44, 35
For the following set of achievement scores, compute the unbiased standard deviation and variance. 87, 87, 58, 78, 98, 69, 88, 71, 86, 91
Now compute the biased estimates for the data in Question 4.Data From Question 4 4. For the following set of achievement scores, compute the unbi- ased standard deviation and variance. (Hint: Use
Why are the unbiased estimates computed in Question 4 larger than the biased estimates computed in question 5?Data From Question 4Data From Question 5 4. For the following set of achievement scores,
This practice problem uses the data contained in the file named. There are two variables in this data set.Using Excel, compute the standard deviation and variance (both biased and unbiased) for
You're one of the outstanding young strategists for Big Boy Airlines and are really curious to compare the number of passengers flying in the mornings versus the evenings out of the Kansas City,
You are conducting an experiment on the effectiveness of a reading intervention with young children and want to report the descriptive results to your colleagues. Some of the children received the
Why would you chose to report the variance of a set of scores rather than the standard deviation?
A data set of 50 comprehension scores (Comp Score). Complete the tasks and answer the questions below.a. Create a frequency distribution and a histogram for the set.b. Why did you select the class
What kind of chart would you use to illustrate the following data?a. The number of students in a school district over a period of 10 yearsb. The proportion of 9th, 10th, and 11 th graders who
For each of the following, indicate whether you would use a pie, line, or bar/column chart and explain why.a. The proportion of freshmen, sophomores, juniors, and seniors in a particular universityb.
Go to the library and find a journal article in your area of interest that contains empirical data but does not contain any visual representation of them. Use the data to create a chart. Be sure to
Create a simple column chart that graphs the sales of an ice cream shop over the summer, fall, winter, and spring seasons. If you can, use an ice cream cone for the column. Now, see if you can easily
Create the worst-looking chart that you can, crowded with chart and font junk. If it's worse than your study buddy's chart, you win.
Create a simple bar chart for number of faculty at different ranks (assistant, associate, and full professor) and label the data sets and include axes and chart titles, minor and major vertical grid
1 . Use these data to answer Questions 1.a. Compute the Pearson product-moment correlation coefficient by hand and show all your work.b. Construct a scatterplot for these 10 values by hand. Based on
Use these data to answer Questions 2a and 2b.a. Using either a calculator or Excel, compute the Pearson correlation coefficient.b. Interpret the relationship between these variables using the
Compute the correlation coefficient for the data below, saved, and interpret the coefficient. We are examining the relationship between the number of years· of training that doctors have and their
Height and weight in humans tend to be correlated because they are the result of lots of similar experiences in an individual's life and the person's genetic traits. Name two variables that may not
Data Analysis tools to compute the correlations between hand-washing efficiency scored on a scale of 1 to 5 with 1 being best (Wash), number of times hands are washed each day (Number), and number of
The coefficient of determination between two variables is .64. Answer the following questions:a. What is the Pearson correlation coefficient?b. How strong is the relationship?c. How much of the
Look back at Table 5.3. What type of correlation coefficient would you use to examine the relationship between ethnicity (defined as different categories) and political affiliation (defined as
When variables are related to each other, why might this be the case? And, when two variables are strongly related to one another, does it mean that a change in one causes a change in the other? Why
You're the director of the local health clinic, and you and the city's school district are conducting a study to examine the relationship between school dropout rate and teenage pregnancy. One of the
For the following set of scores, calculate the Pearson correlation coefficient and interpret the outcome. Budget Increase Number of Clients Served 7% 3% 11% 14% 5% 13% 7% 26% 2% 8%
Rank the following correlation coefficients on strength of their relationship (list the weakest first): +.71 +.36 -.45 +.47 -.62
How do you explain the observation that if parents wave garlic over an infant's crib, the child is likely to begin walking between 18 and 24 months of age? These two events are closely correlated!
Go to the library and find five journal articles in your area of interest in which reliability and validity data are reported. Discuss the outcome measures that are used. Identify the type of
Provide an example of when you would want to establish test-retest reliability and when you would want parallel forms reliability.
Here are the test scores for a group of 15 adults who were assessed on their long-term memory in June and again in August using the same instrument. What type of reliability measure would you use to
The observational data between two judges across 50 days of rating. Would you substitute one judge for the other? Why or why not?
How can a test be reliable and not valid? And why is a test not valid unless it is reliable?
When you are testing any experimental hypothesis, why is it important that the test you use to measure the outcome be both reliable and valid?
Describe the difference between the two types of criterion validity and provide an example of each.
Why is construct validity often so difficult to establish?
Go to the library and select five empirical research articles (those that contain actual data) from your area of interest. For each one, list the following:a. What is the null hypothesis (implied or
While you're at the library, select two other articles from an area in which you are interested and write a brief description of the sample and how it was selected from the population. Be sure to
For the following research questions, create one null hypothesis, one directional research hypothesis, and one nondirectional research hypothesis.a. What are the effects of attention span on
Go back to the five hypotheses that you found in question 1 above and evaluate each using the five criteria that were discussed at the end of the chapter.
What kinds of problems might using a poorly written or ambiguous research hypothesis introduce?
What is the null hypothesis, and what is one of its important purposes? How does it differ from the research hypothesis?
What is chance in the context of a research hypothesis? And what do we do about chance in our experiments? .
Why does the null hypothesis presume no relationship between variables?
Time to be even more creative! Provide one null and one research hypothesis and an equation concerning each of the following:a. The amount of money spent on food by undergraduate studentathletes and
Answer the following questions about normal curves:a. What are the characteristics of the normal curve?b. What human behavior, trait, or characteristic can you think of that is distributed normally?
Why is a z score a standard score, and why can z scores be used to compare scores from different distributions with one another?
What is the primary value of using z scores? Provide an example of how they might be used.
Compute the z scores for the following raw scores where X = 50 and the standard deviation = 5. a. 55 b. 50 c. 60 d. 58.5 e. 46
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