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Statistics Applied With Excel Data Analysis Is An Art 1st Edition Franz Kronthaler - Solutions
9.5 Why does the null hypothesis usually assume no relationship between variables or no difference between groups?
9.6 If interested, read the story “Die Waage der Baleks” by Heinrich Böll and formulate a hypothesis about the story with in mind the weighing machine. Think about how the boy tests his presumption. Unfortunately the book is only available in German.
10.1 Using Excel, draw the normal distribution curves N(−20, 15), N(20, 15) and N(0, 25) and compare them.
10.2 Using the z-transformation, transform the normal distribution N(20, 15) into the standard normal distribution N(0, 1). What are the z values for the following x values:− 25, − 20,− 10,− 7, 5, 20, 35, 47, 50, 60, 65?
10.3 What is the area under the standard normal distribution curve to the right of z= 0.5, 0.75, 1.0, 1.26?
10.4 What is the area under the standard normal distribution curve to the left of z= − 0.5,− 0.75, − 1.0, − 1.26?
10.5 Compare the solutions from Task 3 and Task 4. What do we see?
10.6 Suppose that the age of founders is normally distributed with mean 35 and standard deviation 7.
What is the probability that we discover a founder who is older than 42 years?
What is the probability that we discover a founder who is younger than 21 years?
What is the probability that we discover a founder between the ages of 42 and 49?
10.7 Suppose one of our enterprise founders has developed a novel process to cut panel sheets. The most important thing is the precision of the cutting width. He regularly checks the width and finds that the width of the cuts is 0.1 mm on average, with a standard deviation of 0.005 mm. What is the
10.8 We need to be in the top 5% of students in a selection process to receive a scholarship.We know that the distribution of points on the test is normally distributed, and that there is usually an average of 80 points with a standard deviation of 10.0 points. How many points do we need to score
11.1 What are the two meanings of the significance level α?
11.2 Which of the following statements is correct:
11.3 When to test two-sided, left-sided or right-sided?
11.4 Formulate both the null hypothesis and the alternative hypothesis for the two-sided test, the left-sided test, and the right-sided test for the following research question:What is the age of enterprise founders?
11.5 What is the relationship between the α-error and the β-error?
11.6 Go to the library and find an article of interest that uses data to generate knowledge about the population. Explain how the author used the concept of statistical significance to generate knowledge about the population.
In the test for a group mean, we address the question of whether the assumed mean of the population is in line with our sample finding.
If the sample is large and we know about the standard deviation in the population, the test distribution is the standard normal distribution and our test value is standard normal distributed.
If the sample is small or if we do not know the standard deviation in the population, the test distribution is the t-distribution and our test value is t-distributed.
Cohen’s d is an often used measure to calculate the effect size.
The test for a group mean is often referred to as the one-sample t-test.
12.1 We are interested in the professional experience that enterprise founders have on average. Based on prior considerations and studies we read, we hypothesize that they have typically accumulated ten years of professional experience before starting an enterprise. Accordingly, we formulate the
12.2 One of our companies has grown by an average of 5% in recent years. We are now interested in whether the company has grown below average or above average compared to the population. To test this, we formulate the following null hypothesis:The average growth of young enterprises in the
12.3 Assume that our sample contains only the first 25 firms in our data set. Perform task 2 again for this problem.
12.4 We are interested in whether the proportion that firms spend on marketing has fallen in recent years. We know that ten years ago the expenditure was in average 15%.To test this, we formulate the null hypothesis: The average turnover proportion spent on marketing of young enterprises is greater
12.5 We know that ten years ago, young enterprises spent on average 5% of their turnover on innovation. We hypothesize that this effort has increased as the literature discusses the increasing importance of innovation. We want to test this using the following null hypothesis: The average turnover
In the test for a difference between group means, we address the question whether two groups in their population differ with respect to the average behavior.
The test assumes that the test variable is metric and normally distributed.
If the sample is small and the test variable is metric but not normally distributed, or if the test variable is ordinal, we can use the Mann−Whitney test.
The test for a difference between group means is often called independent samples ttest.
Depending on whether the variances are equal or unequal, we perform the test for equal variances or unequal variances.
13.1 We are interested in whether men and women are of the same age when they start a business. Theoretical considerations and previous studies lead us to assume that men are older than women on average. Perform the test by hand at the 10%significance level, taking into account all relevant steps.
13.2 We are interested in whether industrial firms or service firms growth faster over the last five years. Studies and theoretical considerations suggest that there should be a difference. Perform the test at the 5% significance level, considering all relevant steps. The following values are
13.3 Using Excel, rerun the test from Task 13.2 at the 5% significance level. Compare the results. Take into account any rounding errors.
13.4 We are interested in whether industrial firms or service firms spend more money on innovation. Studies and theoretical considerations indicate that industrial firms spend more. Perform the test at the 1% significance level, considering all relevant steps. The following values are available: xi
13.5 Using Excel, rerun the test from Task 13.4 at the 1% significance level.
13.6 We ask whether men and women have more job experience when they start an enterprise. Existing studies suggest that there is a difference. We perform the test at the 10% significance level, considering all relevant steps. The following values are available: x¯m = 7.2,sm = 3.42, nm = 65, x¯f =
13.7 Using Excel, rerun the test from Task 13.6 at the 10% significance level.
13.8 We are interested in whether male or female founders spend more on marketing.Theoretical considerations lead us to assume that male founders spend more money on marketing than female founders. We conduct the test considering all relevant steps using Excel.
13.9 What values do we need to perform the test for a difference between group means?
13.10 If the test variable is metric but not normally distributed or ordinal, which test is used?
In the test for a difference between means in dependent samples, we address the question of whether a treatment has an influence on people or objects.
In the test for a difference between means in dependent samples, we examine the same people or objects twice, once before and once after the treatment.
The test assumes that the test variable is metric and normally distributed.
For a small sample and metric but not normally distributed data and for ordinal data, we use the Wilcoxon test for dependent samples.
14.1 We are interested in whether a training in accounting results in less time spent per month on accounting (data_accounting.xlsx). Perform the test by hand at the 10%significance level and interpret the result, considering all relevant steps.
14.2 Perform the test from application 14.1 again at the 10% significance level using Excel and compare the results.
14.3 We are interested in whether drinking energy drinks affects the performance of athletes (data_drinks.xlsx). The study design involves the same athletes running as far as they can twice in one hour each time. Once they have the option to consume only water during the run, the other time they
We use analysis of variance when we are comparing more than two groups at the same time.
The analysis of variance is called ANOVA too.
The analysis of variance is an omnibus test, we analyze here if there are group differences between all groups compared, not between which ones.
Following the analysis of variance, a post hoc test should be performed to determine between which groups differences exist.
When groups are compared pairwise, the so-called error inflation occurs, hence an error correction is necessary.
If the test variable is metric but not normally distributed or if the test variable is ordinal, the Kruskal–Wallis test is used.
15.1 Use the first twelve observations of the data set data_workload.xlsx (n = 12) and recalculate the example in the textbook. Test at the 10% significance level whether there is a difference in the workload between the founders with different founding motives.
15.2 We are interested in whether there is a difference in enterprise growth between founders with different levels of education. Use the data set data_growth and test at a significance level of 5% with Excel the null hypothesis: The group means are the same.
15.3 We analyze the question of whether founders with different educational backgrounds spend different amounts of money on marketing. Use the data set data_growth and test at a significance level of 10% with Excel the null hypothesis: The group means are the same.
15.4 Use the data set data_workload.xlsx and analyze whether male and female founders differ in terms of their workload. Test at the 5% significance level using both the analysis of variance and the independent samples t-test. Compare the test results.
16.1 For our data set data_growth.xlsx, calculate the Bravais-Pearson correlation coefficient for the variables growth and marketing for the first eight observations (n = 8)by hand and test the result non-directional at the 5% significance level.
16.2 For our data set data_growth.xlsx, calculate the Bravais-Pearson correlation coefficient for the variables growth and marketing using Excel (n = 100) and test the result non-directional at the 5% significance level.
16.3 For our data set data_growth.xlsx, calculate the Bravais-Pearson correlation coefficient for the variables growth and experience for the first eight observations (n = 8)by hand. Test for a positive relationship at the 1% significance level.
16.4 For our data set data_growth.xlsx, calculate the Bravais-Pearson correlation coefficient for the variables growth and experience using Excel (n = 100). Test for a positive relationship at the 1% significance level.
16.5 For our data set data_growth.xlsx, calculate Spearman’s rank correlation coefficient for the variables growth and self-assessment for the first eight observations (n = 8)by hand and test for a positive relationship at the 10% significance level.
16.6 For our data set data_growth.xlsx, calculate Spearman’s rank correlation coefficient for the variables growth and self-assessment using Excel (n = 100) and test for a positive relationship at the 10% significance level.
16.7 For our dataset data_growth.xlsx, calculate the phi coefficient for the variables sex and sector using Excel (n = 100) and test the result at the 5% significance level.
16.8 For our dataset data_growth.xlsx, calculate the contingency coefficient for the variables sex and motive using Excel (n = 100) and test the result at the 10%significance level.
16.9 We are interested in whether there is a correlation between three stocks and look for the historical values for VW, Daimler and SAP (see Chap. 6). Test at the 5%significance level between which stocks there is a significant relationship.
Test procedures for nominal data are based on frequency analysis.
Test procedures for nominal data are often called just χ2-tests.
For χ2-test procedures cell frequencies should be at least five observations per cell.
17.1 We want to know whether there are differences with respect to the motives to start an enterprise. To do so, we consider the following null hypothesis: all start-up motives occur with equal frequencies. Calculate the corresponding test procedure, test at the 5% significance level and interpret
17.2 We are interested in whether there are differences between men and women with regard to the importance of motives to found an enterprise. Calculate the corresponding test procedure, test at the 5% significance level and interpret the result.
17.3 We are conducting an educational campaign in our company considering nutrition in the workplace. Our goal is to promote a health-conscious diet in the workplace.We are randomly observing 200 employees and asking them about their diet at work before and after the campaign. Using these results,
What factors determine the performance of a football team? Is the overall value of the football team or the presence of a superstar important?
What impact will my marketing have on my sales figures? What happens if marketing expenditure increases?
What impact does research and development have on a country’s innovation rate? What happens when a country increases its spending on basic research?
What effect does development aid have on the growth of developing countries? What happens when development aid are increased?
What effect does violence on television have on young people? What happens when television shows become more violent?
Simple linear regression is used to estimate a linear relationship between two metric variables.
Applying regression analysis requires a theory-driven approach. We need a sound theoretical foundation which shows that the independent variable has an impact on the dependent variable.
The ordinary least squares method is used to estimate the regression line.
The coefficient of determination R2 is a measure of the strength of the relationship.It explains how much of the variance of the dependent variable is explained by the independent variable.
Usually, one independent variable is not enough to explain a dependent variable, i.e., typically more than one independent variable is necessary.
Out-of-sample predictions are based on the assumption that the discovered relationship holds beyond the observation range, and should be applied with caution.
19.1 Why are theoretical considerations necessary before conducting a regression analysis?
19.2 For the first eight companies of our data set, data_growth.xlsx, draw and calculate by hand the scatterplot, the regression line, and the coefficient of determination for the variable growth and marketing. Use the variable growth as the dependent variable and the variable marketing as the
19.3 Using the result from application 2, predict the growth rate for marketing expenditures in the height of 20%. Is there a problem with the prediction?
19.4 For the first eight companies of our data set data_growth.xlsx, draw and calculate by hand the scatterplot, the regression line, and the coefficient of determination for the variable growth and innovation. Use growth as the dependent variable and innovation as the independent variable.
19.5 Using the result from application 4, predict the growth rate for innovation expenditures in the height of 20%. Is there a problem with the prediction?
19.6 Using Excel, draw and calculate the scatterplot, regression line, and coefficient of determination for the following pairs of variables: growth and marketing, growth and innovation, and growth and age (data_growth.xlsx). Use the variable growth as the dependent variable. Interpret the results.
19.7 With task 6 in mind, describe why one independent variable is not sufficient to explain the growth rate.
1. The regression function is well specified and contains all the relevant independent variables. The relationship between the independent variables and the dependent variable is linear.
2. The deviations of the observed Y -values from the estimated Y-values have an expected value of zero.
3. The deviations are not correlated with the independent variables.
4. The variance of the deviations is constant.
5. Two or more independent variables are not correlated.
6. The deviations are uncorrelated with each other.
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