# 6. Hypothesis Testing

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## 56 Questions

### In hypothesis testing, what are we looking for?

A statistically significant difference between two measurements

### What is the purpose of testing the hypothesis that a coin is fair?

To determine if there is a statistically significant difference in the number of heads and tails

### If a fair coin is flipped 100 times and comes up heads 52 times and tails 48 times, is this a statistically significant difference?

No, it is not statistically significant

### If a fair coin is flipped 100 times and comes up heads 32 times and tails 68 times, is this a statistically significant difference?

Yes, it is statistically significant

H0

### What does the alternative hypothesis represent in hypothesis testing?

Yes, there is a difference between population A and population B

### What is the purpose of A/B testing?

To determine which version has the most impact in meeting business goals

Control

### What is the focus of A/B testing?

Statistically significant improvements in measured data

### What is the primary goal of A/B testing?

To determine a 'winner' and a 'loser' based on statistically significant improvements

Variation

### What does the determination that color makes a difference in sales confirm?

The alternative hypothesis

### What are the two mutually exclusive hypotheses in hypothesis testing?

Null hypothesis and alternative hypothesis

### What do hypothesis tests aim to determine?

Which hypothesis—the null or the alternative—is the true one

### What is the alternative hypothesis commonly referred to as?

The alternative hypothesis

H0

Alpha value

### What motivates the formation of hypotheses in marketing analysis?

Evaluation questions

### What do evaluation questions in marketing analysis often reduce to?

Questions of difference

### What are the null hypothesis and the alternative hypothesis used to evaluate?

Presence of a difference

### What is the formula for calculating a confidence interval in Excel or Google Sheets based on?

Alpha value, sample size, and standard deviation

Hypotheses

Alpha value

Data analysis

### What do evaluation questions in marketing analysis often reduce to?

Simple question of whether there is a difference

### What are confidence intervals based on?

Probabilities and sample sizes

### What does hypothesis testing involve?

Null hypothesis and alternative hypothesis

### What does a low p-value indicate?

A low probability of chance and a high probability of statistical significance

### What is the purpose of the alpha value in statistical analysis?

To set the boundary for acceptable p-values in an analysis

### What is the standard assumption for the alpha value in statistical analysis?

$\alpha = 0.05$

### What does a lower alpha value indicate in statistical analysis?

Higher confidence in the analysis

### What do confidence intervals establish in statistical analysis?

A range of precision for calculated values

### What does a 95% confidence interval for a fair coin indicate?

A 95% confidence that the observed outcome will fall within the interval

4%

### What is the T-test method used for in statistical analysis?

Calculating a p-value

### What does a statistically significant difference in data indicate?

An effect worthy of further investigation

### What does the P-value represent in statistical analysis?

The probability that a difference between two data measurements is due to random chance

### What is the purpose of a 95% confidence interval for a fair coin in statistical analysis?

To establish a range of precision for the expected outcomes

The alpha value

### What is a 'false positive' in the context of testing a hypothesis?

When data seems to confirm something is true, but it is false

### What is the main reason for the possibility of errors in statistical analyses?

Statistical analyses are ultimately based on probability

### What is the consequence of not conforming to ideal conditions like perfect randomization in statistical analyses?

A small chance of errors in determining the hypothesis from the data

### What is the key factor leading to errors in determining a hypothesis from marketing data?

Statistical analyses are based on educated predictions and probability

### What is a Type I error in hypothesis testing?

Rejecting the null hypothesis when it is true

### What is a Type II error in hypothesis testing?

Accepting the null hypothesis when it is false

H0

H1

False positive

False negative

### What does a Type I error lead to in hypothesis testing?

Incorrectly concluding a difference when there isn't one

### What does a Type II error lead to in hypothesis testing?

Incorrectly concluding no difference when there is one

### What is the first hypothesis typically referred to as in hypothesis testing?

Null hypothesis (H0)

### What is the second hypothesis typically referred to as in hypothesis testing?

Alternative hypothesis (H1)

Type I error

Type II error

## Study Notes

Confidence Intervals and Hypothesis Testing in Marketing Analysis

• Confidence intervals are based on probabilities and sample sizes and can be calculated for any degree of confidence, not just 95%.
• The alpha value (𝛂) sets the degree of variance around the calculated value that stakeholders are willing to tolerate.
• The percentage of the confidence interval is determined by the alpha value, e.g., a 95% confidence interval is based on a 5% alpha value (𝛂 = 0.05).
• The formula for calculating a confidence interval in Excel or Google Sheets includes the alpha value, sample size, and standard deviation.
• An example calculation of a 95% confidence interval for weekly sales data in a spreadsheet is provided, showing a range of likely sales values.
• Hypotheses are proposed answers to evaluation questions in marketing analysis and are tested through data analysis.
• Evaluation questions in marketing analysis motivate the formation of hypotheses, such as whether website color affects sales.
• Evaluation questions often boil down to a question of difference, such as differences between demographic groups in purchasing behavior or the cost-effectiveness of advertising.
• Hypotheses address questions of difference, like whether there is a difference in sales between different website colors.
• Hypothesis testing involves the null hypothesis (H0) and the alternative hypothesis (H1) which are used to evaluate the presence of a difference.
• Evaluation questions in marketing analysis often reduce to the simple question of whether there is a difference, such as differences in purchasing behavior or campaign effectiveness.
• The formation of hypotheses and hypothesis testing are integral parts of marketing analysis, addressing questions about differences and effects.

Understanding P-Values, Alpha, and Confidence Intervals

• A statistically significant difference in data can indicate an unfair coin or an effect worthy of further investigation.
• P-value represents the probability that a difference between two data measurements is due to random chance.
• P-value is usually calculated by software and expressed in decimal form.
• A low p-value indicates a low probability of chance and a high probability of statistical significance.
• The T-test method is one way to calculate a p-value.
• A p-value of 0.04 means there is a 4% chance the measured difference occurred by chance.
• The acceptable p-value is determined by the alpha value, which sets the boundary for acceptable p-values in an analysis.
• A lower alpha value means higher confidence in the analysis.
• A standard alpha assumption is 5% (𝛂 = 0.05) for acceptable significant difference.
• Conﬁdence intervals establish a range of precision for calculated values, giving a specific degree of confidence that observed results will match the calculation.
• For a fair coin, the 95% confidence interval for flipping tails is 10 flips out of 100, meaning there's a 95% chance tails will come up within 10 flips of the statistical mean of 50 flips.
• The 95% confidence interval for a fair coin indicates a 95% confidence that it will come up tails somewhere between 40 to 60 times.

Test your understanding of confidence intervals, hypothesis testing, p-values, and alpha values in marketing analysis with this quiz. Assess your knowledge of how these statistical concepts are applied in evaluating data, forming hypotheses, and making informed marketing decisions.

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