## Hypothesis Testing for the Single Population where the Population variance is Unknown

- Problem: You are a marketing analyst. Estimate if the competitor has a higher open rate.
- Open Rate: Measure of how many people on the email list actually opened an email
- Refer Here for the dataset
- The average open rate of your organization is 40%
- Null Hypothesis H0: μ <= 40%
- Alternative Hypothesis μ > 40%
- Lets use the significance level of 5%
- Lets try to calculate T-Score
- Now lets calculate critical value with population variation unknown (t-distribution)
- significance level = alpha = 0.05
- degrees of freedom = number of samples -1 = 10-1 = 9
- t-value with alpha 0.05 and 9 degrees of freedom

- Decision Rule:
- Accept if the absoulte value of T score is less than critical value
- Reject if the absolute value of T-Score is greater than critical

- |t| = |1.83| = 1.83
- |T| = |-0.53| = 0.53
`T-score < critical value t`

So we accept the null hypothesis- Also p-score > significance level So we accept the null hypothesis
- Exercise: Test at 1%, 5% significance level.
- Null Hypothesis is Open rate is 40%
- Alternative Hypothesis is Open rate is not 40%
- Prove the test results using T-score and critical and also use P-Value
- Validate if the below analysis is correct

- Two sided t-value distribution Refer Here

## Multiple Populations

- Dependent Samples:
- Lets go with Magnesium samples for 10 patients which we have used in CI.
- We would like to know if the medicine works
- Null Hypothesis: Medicine doesnot increase magnesium levels
- Alternative Hypothesis: Medicine increases magnesium levels
- Refer Here for the Dataset
- Decision Rule
- Accept if
`p > α`

- Reject if
`p < α`

- Accept if
- Results:
- We cannot conclude with the current samples whether to accept or reject the null hypothesis => Get More samples and work in the Lab towards your medicine.