Data Science Classroom Series – 18/Nov/2021

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 Preview Preview
    • 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 Preview
    • 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 Preview
    • 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 Preview
    • 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 Preview
    • Refer Here for the Dataset Preview
    • Decision Rule
      • Accept if p > α
      • Reject if p < α
    • Results: Preview
    • 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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