## 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`
• 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.

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