BS termer Flashcards
What is population?
In business statistics, a population is the entire group of people, items, or data that you are interested in studying.
It includes everything or everyone you want to make conclusions about.
Example:
If you’re studying customer satisfaction for a company, the population could be all of the company’s customers.
Population refers to the whole group, not just a sample or part of it.
what is The central limit theorem (CLT)
The Central Limit Theorem (CLT) says that if you take many random samples from any group (population), the average of those samples will form a normal (bell-shaped) curve, even if the original group isn’t normally distributed.
Simple Example:
If you measure the height of many groups of people, the average height of each group will follow a bell curve, no matter how the heights are spread out in the full population.
This helps us use sample data to make predictions about the whole population.
What is hypothesis testing?
Hypothesis testing is a way to use data to check if an idea or claim is likely to be true.
Simple Steps:
1.Start with a claim (called a hypothesis).
Null hypothesis (H₀): Nothing has changed, or there’s no effect.
Alternative hypothesis (H₁): There is a change or effect.
2.Collect data and analyze it.
3.Make a decision:
If the data supports the change, reject the null hypothesis.
If not, keep the null hypothesis.
Example:
You want to test if a new product lasts longer than the old one. The null hypothesis says there’s no difference. You test the products, and if the new one lasts longer, you reject the null hypothesis.
what is matched sample design (Hypothesis testing)
Matched sample design in hypothesis testing is when you compare two sets of data that are related or paired in some way, often from the same people or subjects. This is done to see if there’s a difference between two conditions or treatments.
Example:
A company wants to test if a new training program improves employee performance. They measure the performance of the same employees:
Before the training (first set of data)
After the training (second set of data)
Each employee’s performance is compared before and after the training, so the data is “matched” because it comes from the same people in both conditions. This helps check if the training caused a real improvement in performance.
How can you make the confidence interval smaller?
- Increase the Sample Size:
Collect more data. A larger sample size gives more information, which reduces uncertainty.
Effect: More data points lead to a more precise estimate, thus narrowing the confidence interval.
- Reduce Variability:
Control the conditions under which data is collected to minimize variability or errors.
Effect: Less variability in data leads to a narrower interval.
- Lower the Confidence Level:
Choose a lower confidence level (e.g., 90% instead of 95%). This means you’re accepting more risk of being wrong, but the interval will be smaller.
Effect: Lowering the confidence level decreases the width of the interval.
what is ordinal scale of measurement?
An ordinal scale is a way to rank or order things. It tells you the position of something, but it doesn’t tell you how much better or worse one thing is compared to another.
Simple Features:
You know the order, like 1st, 2nd, 3rd.
You don’t know how big the difference is between the ranks.
Example:
A survey asks: “How happy are you?”
-Very happy
-Happy
-Neutral
-Unhappy
-Very unhappy
You know the order, but you don’t know how much happier “Very happy” is than “Happy.”
So, ordinal scales rank things but don’t measure exact differences.
what is nominal scale of measurement
A nominal scale of measurement is the simplest way to classify data. It involves labeling or naming categories without any order or ranking. The categories are just different names or labels, and there is no specific order between them.
Key Features:
Categories are just names or labels (no ranking).
You can tell if two items are in the same or different category, but that’s it.
No numerical value or order.
Example:
Favorite colors: Red, Blue, Green.
Types of fruits: Apple, Banana, Orange.
In this case, the colors or fruits are simply categories. There’s no order or ranking between them; they are just different labels.
what is an interval scale of measurement?
An interval scale is a way to measure things where:
Order matters: You can rank the values.
Equal differences: The difference between values is the same. For example, the difference between 10 and 20 is the same as between 30 and 40.
No true zero: A zero point doesn’t mean “none” of what you’re measuring. For instance, 0 degrees Celsius doesn’t mean there’s no temperature.
Simple Example:
Temperature: If it’s 20°C and 30°C, the difference is 10 degrees. But 0°C doesn’t mean there’s no temperature; it just means it’s freezing.
So, an interval scale helps you compare how much more or less there is, but it doesn’t have a true zero point.
What is a ratio scale of measurement?
A ratio scale of measurement is the highest level of measurement that allows you to compare quantities and make meaningful statements about the differences and ratios between values. It has all the features of an interval scale, but with the added benefit of having a true zero point.
Key Features:
Order: Values can be ranked.
Equal Intervals: The difference between values is consistent.
True Zero: A zero point indicates the complete absence of the quantity being measured. For example, 0 means “none.”
Examples:
-Height: If someone is 0 cm tall, that means there is no height.
-Weight: A weight of 0 kg means there is no weight at all.
-Income: An income of $0 means no money earned.
Summary:
In a ratio scale, you can say that one value is twice as much as another. For example, a weight of 10 kg is twice as heavy as 5 kg. This scale allows for the most detailed and meaningful comparisons.
what is an mutually exclusive event?
Mutually exclusive events are events that cannot happen at the same time. If one event occurs, it means the other event cannot occur.
Key Features:
No Overlap: There is no intersection between the events; they do not share any outcomes.
Only One Outcome: In a single trial, only one of the mutually exclusive events can occure
examples:
Coin Toss: When you flip a coin, the outcomes “heads” and “tails” are mutually exclusive. You can’t get both heads and tails on the same flip.
Rolling a Die: When rolling a six-sided die, getting a “3” and getting a “5” are mutually exclusive events. You can only roll one number at a time.
Summary:
If two events are mutually exclusive, the occurrence of one event means the other cannot happen, making their probabilities additive. For example, if the probability of event A is 0.3 and the probability of event B is 0.4, then the probability of either event A or event B occurring is 0.3 + 0.4 = 0.7 (assuming A and B are mutually exclusive).
What is the difference between combinations and permutations?
- Combinations:
Order Does Not Matter: It’s about selecting items without caring about the order in which they are selected.
Example: If you have a fruit bowl with an apple, banana, and orange, choosing an apple and banana is the same as choosing a banana and apple. The selection is the same.
- Permutations:
Order Matters: It’s about selecting items where the order is important.
Example: If you have the letters A, B, and C, arranging them as AB and BA are considered different arrangements. The order makes a difference.
Summary:
-Combinations: Selection without regard to order (e.g., choosing ice cream flavors).
-Permutations: Arrangement with regard to order (e.g., arranging books on a shelf).
what is type 1 and type 2 errors
Type I Error:
Definition: A Type I error happens when you reject the null hypothesis (claiming there is an effect or difference) when it is actually true. In simple terms, you think something is happening when it really isn’t.
Example: Imagine a doctor tests a patient for a disease and the test result is positive (indicating the patient has the disease). If the patient actually does not have the disease, but the doctor concludes that they do, that’s a Type I error. The doctor wrongly claims the patient is sick when they are healthy.
Type II Error:
Definition: A Type II error occurs when you fail to reject the null hypothesis (thinking there is no effect or difference) when it is actually false. This means you think nothing is happening when there actually is.
Example: Using the same doctor scenario, if the test result is negative (indicating the patient does not have the disease) but the patient actually does have it, that’s a Type II error. The doctor misses the actual illness.
what is independent events
Imagine you have a standard deck of 52 playing cards. You draw one card and then roll a six-sided die.
Event A: Drawing an Ace from the deck.
Event B: Rolling a 4 on the die.
Explanation:
The outcome of drawing a card (whether it’s an Ace or not) does not affect the outcome of rolling the die (whether you roll a 4 or not). They are completely separate events.
In this example, drawing a card and rolling a die are independent events because the outcome of one does not influence the outcome of the other. You can successfully calculate the probabilities without them affecting each other.
What is anova testing?
An ANOVA table is used in statistics to organize and display the results of an Analysis of Variance (ANOVA) test, which compares the means of three or more groups to see if they are significantly different from each other.
what is a discrete random variable
A discrete random variable is a type of variable in statistics that can only take on specific, distinct values (usually whole numbers). These values are countable and there are gaps between them.
Key Features:
Countable values: A discrete random variable can only take certain values, like 0, 1, 2, 3, etc. It cannot take on any value between these points (e.g., no decimals or fractions).
Random: The value it takes is determined by chance.
Examples:
Rolling a Die: The outcome (1, 2, 3, 4, 5, or6) is a discrete random variable because you can only get one of these specific values.
Number of Customers: If you’re counting the number of customers entering a store in a day, it can be 0, 1, 2, 3, etc. You can’t have 1.5 customers, so this is also a discrete random variable.
what is a continous random variable
A continuous random variable is a variable that can take on any value within a given range, meaning it can have infinitely many possible values. These values are not countable because they can be fractions, decimals, or whole numbers, and there are no gaps between the possible values.
Key Features:
Infinite values: A continuous random variable can take any value within a range, including decimal and fractional values.
Measured, not counted: Continuous random variables often represent things that are measured, like time, weight, height, or temperature.
Examples:
Height: If you’re measuring the height of people, it can be 170 cm, 170.5 cm, or any number in between.
Time: The time it takes to complete a task could be 2.3 minutes, 2.31 minutes, or any fraction of time.
Temperature: Temperature can be 20°C, 20.1°C, or any value in between.
Summary:
A continuous random variable can take on any value within a range and is often used to model measurements like time, distance, or weight, where precise values can be infinitely small.
