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.