a. Construct a 2 ×2 contingency table, using fees as the row variable and type as the column var

step 1 Once again, welcome to a new problem. This time we're dealing with descriptive statistics. And d

A. Construct a 2 ×2 contingency table, using fees as the row...

Key Concepts

Contingency Table

A contingency table is a matrix used to display the frequency distribution of two categorical variables. It organizes data into rows and columns representing different categories, which helps in visualizing the association between the variables and is a fundamental tool in statistical analysis for categorical data.

Chi-Square Test of Independence

The chi-square test of independence is a statistical method used to determine whether there is a significant association between two categorical variables. By comparing the observed frequencies in a contingency table to the frequencies that would be expected if the variables were independent, the test evaluates if any association exists beyond what could be attributed to random chance.

Hypothesis Testing

Hypothesis testing in the context of a chi-square test involves setting up a null hypothesis (that there is no association between the variables) and an alternative hypothesis (that the variables are associated). Statistical evidence is then evaluated against a predetermined significance level to either reject or fail to reject the null hypothesis.

Significance Level

The significance level, often denoted by alpha (?), is the threshold used to determine whether an observed effect is statistically significant. A common choice is 0.05, which means there is a 5% risk of rejecting the null hypothesis when it is actually true. This level helps in making decisions in hypothesis testing by defining the criteria for determining the likelihood that the observed data could be due to chance.

Transcript

00:02 Once again, welcome to a new problem.

00:07 This time we're dealing with descriptive statistics.

00:11 And descriptive statistics is a branch of statistics that uses tables, uses graphs, and also uses numbers.

00:27 And so in terms of numbers, you could have measures of central tendency.

00:32 So we have measures of central tendency.

00:38 And then we also have measures of spread, so central tendency and spread.

00:46 Central tendency numbers include things like the mean, the median, and the mode, and then measures of spread include things like the range, the standard deviation.

01:00 I need to change this a little bit.

01:03 The standard deviation.

01:08 And of course, the interquotile range, iqr, which is the interquotile range.

01:16 And this typically tells us the difference between the third quartile, which is the same as the 75th percentile, and the first quartile, which is the 25th percentile, so that's the difference.

01:40 That's the difference, the third quartile and the in the fast quartile.

01:50 So those are the two things that we're dealing with in this particular problem.

01:57 Now, when it comes to graphs, we have different types of graphs.

02:05 We have the qualitative graphs.

02:08 For example, bar graphs, and then also we have quantitative graphs.

02:18 For example, the scatter plot, the scatter plot.

02:24 So in this particular problem, we are supposed to look at the data.

02:30 So we have data, the available data, available data, shows information shows the information on profit compared to compared to stockholders equity profit compared to stockholders equity so so if we have profit compared to stockholders equity.

03:25 So stockholders equity, remember this is the investment that shareholders are introduced into a new company.

03:43 So this is what the shareholders introduce into a new company.

03:48 So we want to see, you know, if they put more investments what's going to happen to the profit so in part a but a was saying create create a scatter plot we eat a scatter plot showing showing the relationship between between the various between the variables profit and stockholders ' stockholders ' equity.

04:37 So we want to see those two relationships.

04:40 And then in part b, explain the relationship, explain the relationship between these two variables...

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